Yes, you can make the cake without an oven. Some veg cake without batter can create easily. You can check out at http://www.askprob.com/forums/topic/how-to-make-veg-cake-at-home/.
If you are looking for batter cake without an oven, use a pressure cooker. First, create your batter or material for cake.
Now put a stand inside the pressure cooker or a tiny inverted vessel. Put a small amount of water beside the vessel.
Place the batter filled dish over the stand. I have attached the image of it have a look at it.
Close the pressure cooker but do not keep the weight above the top. Cook the batter on the medium flame for 30–40 minutes.
Remove the lid of the pressure cooker and poke a small stick or toothpick. If it returns means the cake is ready to serve.