I've never sone it, but here's what I would try. Fit a pastry bag with a Large round rip (maybe even the Bismark so you can reach to the bottom of the pan.) fill your cake pan with the basic batter, then in random places, pipe the colored batter in. You would need to push the tip down into the batter.
Please let us know how it goes, what you did, and a picture. This sounds like a neat idea you have!