Preheat the oven to 350F. Grease a 9x13 baking dish.
In a large mixing bowl, combine cake mix, eggs, water, and oil and whisk to combine. Divide batter evenly between 3 bowls. Add a few drops of each food coloring into the different bowls to end up with pink batter, purple batter, and green batter.
Using a spoon, drop spoonfuls of each colored batter around the baking dish being sure to alternate colors throughout making sure not to mix the colors too heavily.
Bake for 30 minutes or until a cake tester comes out clean. Let cool for 10 minutes.
While the cake cools, combine the pudding mix and milk and whisk to combine until it begins to set, about 5 minutes.
Using the blunt end of a wooden spoon, poke holes in the cake about an inch apart. Pour the pudding over the top of the cake, smoothing out with a spatula.
Cover the cake with Cool Whip and then sprinkles and refrigerate until ready to serve.