Molasses is used for a lot of things, including amimal food and as a food additive for human consumption.
But in this article, discussion of this product (mainly from sugar cane and beets) is limited to food for MICROBES. Yes, molasses can feed microbes in lots of different environments, but the only environments discussed herein, are for composting and in an organic garden.
In this context, there are two basic types of molasses available: sulfured and unsulfured. Basically treating molasses with sulfur results in fortification of iron, calcium and magnesium.
So the question is, do microbes and/or plants need supplemental iron, calcium and magnesium from molasses, to prosper in soil or dirt?
In this author's opinion, no. But some organic gardeners use sulfured molasses in their drenches because they feel plants will appreciate the fortification. However, I think there are better ways to accomplish such fortification than spending the extra money for the sulfured type.
Cane or Beet
Is cane molasses any better than beet molasses? Based on research I've studied, and considering its use to feed microbes, I think the best price should rule that decision. Both types have about the same number of calories as sugar - about 16 calories per teaspoon (5 ml).
Molasses to boost soil microbial activity has been talked about for many decades and the theory has been that it provides an energy source for microbes that can be utilized equally well by all soil organisms.
However, field applications that I have studied, have not tended to produce many convincing responses. For instance, Recent research by SWEP laboratories, has begun to shed light on this issue by looking at soil biology from a balance perspective (according to the principles of the Mikhail System) that has shown some significant effects on soil biology, but are now finding that the soilfoodweb is much more complex than expected - something Dr. Elaine Ingham (www.soilfoodweb.com) could have told them many years ago.
Results of these studies appear to indicate that the lowest application rates work best for fungi and cellulose utilizers, while some bacteria showed the opposite response, with activity increasing as the application rate increased. So my 'take' on this is that BALANCE is the prerequisite to consider, involving the type of microbes you want to supply, based on what you are attempting to accomplish.
With regard to feeding compost tea microbe population (liquid environment, not solids), in my opinion there is no equal in the field, to Dr. Ingham. However, tea must be aerated and fed more than just molasses to accomplish such objective effectively. 
Reheating a 1st Turn
So regarding practical application to compost piles, my advice is to restrict application of molasses to feedstock that you want to REHEAT - basically limited to a first-turn aeration, using a screening technique and applying the mixture to each 6" layer, at no more than one QUARTER cup per 25 square feet of surface area, in sufficient water to thoroughly moisten the entire layer. And yes, the layering technique does mean the more water accumulates in the lower portion of the pile, particularly if extracting the excess moisture as tea. If that is the case, I recommend collecting and reapplying 1st turn tea back onto the pile to concentrate it, and strengthen the leachate, which will contain a molasses constitute, ready for aeration to multiply the microbes present in the tea.
Consider Molasses into the C:N Ratio
If you apply molasses to an initial pile build, remember to factor-in that constituent to the C:N ratio. For collection of tea from an initial pile build, and from subsequent (2nd turn; 3rd turn, etc.) collections, I recommend only adding molasses INTO the tea brewer (with the leachate or compost-mix, and only at the rate recommended by the manufacturer of the brewer - unless you already have extensive experience in brewing compost tea with your machine.
Molasses is CARBON
Molasses is an effective, quick source of carbon energy for various forms of microbial life in a compost pile or gardening dirt. In fact molasses has long been a part of the common products used by organic gardeners to bring greater health to their soils and plants, because it's a great source of carbohydrates that stimulates the growth of beneficial microorganisms.
Types of Molasses
There are many grades and types of molasses, depending upon the maturity of the sugar cane or sugar beet, and the method of extraction that they undergo. The different types are: first molasses, second molasses, unsulfured molasses, sulfured molasses, and blackstrap molasses.
You should also know about DRY molasses which is something different altogether, and is not discussed in this article (see: Dry Molasses). But just so you know, dry molasses is molasses that has been sprayed onto grain residue which acts as a "carrier, and is used by many composters because it is easy to broadcast onto to a feedstock layer without mixing in water, so a square footage/depth of application is then simply watered-in as needed, for appropriate feedstock moistening.
The Best Type for Boosting Fertilizer
For organic gardeners, I recommend unsulfured cane blackstrap molasses as the best choice because it is the most nutritionally (trace elements) valuable of the various types of molasses.
I do not recommend using synthetic chemical fertilizers, but I would be remiss not to mention that molasses is also a chelating agent, which means that it can 'help' convert 'some' chemical nutrients into a form thatís 'more' easily available for organisms and plants to use.
Molasses can be an important addition to an organic fertilizing program (drench or foliar), depending on whether your garden dirt is in need of such. Most organic garden beds worked by folks who actively compost - and use their compost on their garden - do not need molasses, but then, it can be (in minor amounts) added to compost tea when used as a foliar spray directly on plants - a highly recommended practice, especially if the tea is direct leachate and not brewed tea.
Basic Drench Mixture:
1 to 3 tablespoons (15 to 45 ml) blackstrap molasses (unsulfured) per 1 gallon (3.8 liter) of liquid fertilizer mix (this can be any liquid fertilizer, compost tea, kelp, or alfalfa meal tea)
Molasses and Alfalfa Tea Mixture:
4 gallons (15.2 liter) of water
1 cup (225 ml) of fine ground alfalfa meal
1 tablespoon (15 ml) blackstrap or sugar beet molasses
Allow this to sit for 24 hours, and then it is ready for application as a soil drench.
As a foliar feed, recommend straining the mixture so there is nothing to clog the spray head.
© Robert C. Moore ~ All Rights Reserved
Text from Dr. Elaine Ingham:
Bacteria grow well and rapidly on simple sugars to exclusion of any fungus, until sugar concentration becomes extremely high. The simple preservative effect with molasses is the high concentration of sugar. Most organisms cannot grow in the high concentration of sugar. Once a container of molasses is sealed, however, condensate can form on the under-side of the lid if the container suffers heating cooling cycles. As the water drips into the top layer of the molasses concentrate, the sugar content can be diluted enough to allow fungal or actinobacterial growth as a surface scum. Just skim off the surface scum before use in soil, compost, or tea. Do not feed to animals or humans after a surface scum has formed unless you can recognise the organism as non-harmful.
Addition of foods that cause rapid bacterial growth can tie-up nitrate nitrogen so fast, and so effectively that plant growth can be harmed, and even stopped. Bacteria win in competition with plants for N in soil, and thus plants can be killed as the result of lack of N. Of course, the solution to this problem is NOT to kill the bacteria, but rather to establish normal nutrient cycling processes once again. How? Get the protozoa and bacterial-feeding nematodes back to work!
Non-sulphured, Black-strap Molasses: Contains no preservative other than the high concentration of sugar. Black-strap molasses contains about 150 different kinds of sugars, from simple to somewhat complex to humics. During the extraction of sugar, heating results in condensation of the sugars into humic-like substances. The majority of foods in molasses are bacterial foods, but a few are fungal foods. Fungi tolerate high concentrations of sugar better than bacteria, so extremely high concentrations of molasses favour fungi. Testing must be performed to assess what concentration is needed to select for fungi and against bacteria in any particular set of conditions. Testing is also needed when using as a nitrate-to-bacterial biomass converter.
Weed control is often STARTED with addition of molasses to tie-up the excess nitrate helping to set the stage in the soil to grow weeds, and not the plants you want to grow. Assess the calcium situation as well, however, because if you add molasses to grow lots of bacteria, and your soil has poor structure, you may just drive the soil into reduced oxygen conditions, which can result in plant death as well. As Arden Anderson says, "No number is right until all numbers are right". Or as Elaine Ingham says, "What's the most important organ in your body? And you can stay alive with just that one, most important item? You need all your organs, right? Soil needs all the organisms, in the right numbers and right balance and right function".
Organic Molasses: No strong acids or bases, nor extremely high heat are allowed in the production of organic molasses. No preservatives can be used. Because of the lower temperatures used, less condensation of the sugars occur, so fewer condensed, humic materials are present compared to non-sulphured, black-strap molasses
Feed Grade Molasses: Commercial grade molasses has sulphur and possibly other preservatives and antibiotics added to reduce fungal growth. Sulphur in most inorganic forms make excellent fungal inhibitors. Antibiotics will inhibit, kill and prevent the growth a wide range, but not all bacteria and fungi. Thus feed grade molasses is not a good choice for a biological stimulant. Care must be taken to read about the ingredients so no ugly little surprises confront you and you don't get the response you want to see.