If you don't have oven you can cook by old school method.
In India While i was growing up we don't have Oven at home but we still have cake.Try this technique for baking cake with out oven,
Things u need:
1)Thick Aluminium Tall Pan with lid.Some thing like the shape of below image
2)Two Aluminium flat Pans which should fit one on top of another and that can fit into the tall aluminium pan.
3)Sand 1 gallon or the amout to fill one pan.
1) Fill one flat pan with sand and place it inside the aluminium tall pan and heat it in stove.
2)The sand should get very hot.
3)Now put your cake batter in another flat pan and place it on top of the sand pan and cover the tall aluminium pan and bake it till the skewer when pierced on the cake comes out clear.
I have never tried this on my own , but this is the type of pan i used to have in my home.
I Think u can also try this with other type of pan other than aluminium. Dont use black color pan this will brown your cake too much.