If you want it to look nice, the only way to do a cake like that is to make the batter, split it into how many colours you want, colour each lot of batter and bake each layer separately.
They won't take long to cook, and any other method is just going to leave you with a murky mess of a cake.
I have made the standard round, vertically stacked cake. I made the batter, weighed it and then separated the batter into individual bowls, weighing them so that all the layers would be the same size. I used 2 good quality round non stick tins, the cakes cooked really quickly, 8 minutes I think. then I turned them onto wire racks to cool while using the tins for the next layer. the cakes cooled really quickly too.
for that cake I would probably buy 2 small square tins from a specialty cake decorating shop, or victorias basement if they had them because they can be quite cheap. then you know that the layers would all be the same size, making construction a breeze
eta. just found a 10cm square tin online for about $18. that was just looking at one website, you might be able to find cheaper or be able to higher a couple of tins for a day
Edited by imamumto3, 18 January 2013 - 06:29 AM.