Yes, you can make a cake without an oven. Cakes can be made on the top of the stove or in a microwave oven. To make a cake in an oven is quite easy; you simply pour the cake batter into the baking pans and let the batter bake for the prescribed amount of time.
To make a cake in a microwave oven is very similar to making a cake in an oven. But, to make a cake on top of the stove is a lot more complicated, requires steamer baskets or double boilers and results in many dishes that have to be washed.