The council needs to save £25m in 2017-18 alone by either increasing council tax, using reserves, capping school budgets or cutting services.
Councillor Chris Weaver said protecting residents from the brunt of the cuts was "getting harder every year".
The council has already made £200m of savings in the past 10 years.
Its budget stands at £587m, but almost 65% of this is spent on schools and social services.
Both areas face rising demand pressures as the city's population grows and the council's Budget Strategy Report will go before cabinet on Thursday.
Mr Weaver, cabinet member for finance, said: "There's no getting away from it, bridging this budget gap will be very challenging indeed, especially in light of the savings the council has made over the past few years.
"There are some services which may have to go or will only be saved through partnership working with residents or other organisations, or finding new ways to cover costs."
Services may be axed as Cardiff Council faces cutting £74m from its budget over the next three years, the authority has warned.