Betty Crocker "Stir 'n Bake" Cake Mixes.
Use 1/3 cup mix with 2 tablespoons water, mix and bake for 15-20 minutes in the Easy Bake. One box of mix costs around $1.80 and makes 4-5 cakes.

Pillsbury "Sweet Rewards" brownie mix also works well. Use the same ratio of mix to water.

Check your local grocery for any mix that uses only water, no eggs. The eggs are the messy part and little ones that eat the batter could risk food poisoning. I explored making my own mixes but the powered eggs were too hard to come by in small quanities, but I'm still looking.

Good luck, Dr. Gert in Toledo, OH