I've never done it but you might want to PM Macsmom. She makes a rainbowlicious cake that's the same thing.
It's super easy! Make your favorite white cake batter. Divide into 3 or 4 equal portions. Dye the divided batter. Pour in random splotches in pan. Gently swirl with a butter knife or rubber/silicone spatula. Bake as usual. I think it looks best if you leave 1 portion of the batter undied.
Wow this sounds interesting! I think I'm going to try this.