Everything that is known about Mind Flayers' diet details their consumption of humanoid brains. Mind Flayers are physically capable of eating animal brains, but doing so would give them little to no nourishment.

Can mind flayers eat anything other than brains?

As far as I've been able to research, they ONLY eat humanoid brains. Illithids generally live in the Underdark which is far more than just a cave, it is an entire ecosphere that (depending on world details) contains just as much living space as the above-ground world.

How often does a mind flayer need to eat?

Typically, mind flayers consume somewhere between the minimum of one brain per month and the ideal of one brain per week, averaging one brain every two weeks and supplementing their diet with other foods.