My brother-in-law had a small request for his 20th birthday: he came across a rainbow batman shaped cake on the internet and wanted one... so I made one (actually two but you never count the first failure... or at least I'm not going to in this case!)
You can use any cake mixture you like. I used a simple vanilla butter cake recipe six times, each batch with a different colour. Make sure you have sturdy sheet pans that don't buckle in the heat of the oven. My first try this happened and resulted in lop-sided layers and was not good. You'll need plenty of colouring in each batch to make the colours really vibrant. Don't over mix the cake mixture otherwise they'll be tough and rubbery. I layered each sheet with strained warm apricot jam as they came out of the oven, one at a time. I didn't wait for each layer to be cool, instead, i just flipped each onto the previous. After you have all the layers ready, you can begin shaping your cake, or leave it as one big piece, it's up to you.
After cutting into your desired shape, transfer the cake carefully to a cooling rack and cover the entire cake in ganache or buttercream and leave to set. Then, carefully transfer the finished cake to your serving plate. It looks cool on a yellow background, but since I couldn't find one in time, I flipped over a clean baking sheet, covered in tin foil and presented it on that.