Preheat the oven to 350°F and grease a 9x13 baking dish.
In a large mixing bowl, use an electric mixer to beat cake mix, water, egg whites, oil, sour cream, and clear vanilla extract. Mix on low speed for 30 seconds or until combined. Scrape the edges of the bowl. Beat on medium speed for 2 minutes more, scraping the edges occasionally.
Pour 2 cups of the batter into the prepared pan.
Divide the remaining batter between 3 medium bowls (about ½ cup each). Add a few drops of blue, pink, and yellow food coloring (one color per bowl) to the batter, stirring well after each drop, until the batter reaches the desired color.
Place spoonfuls of each colored batter in random places on top of the white batter. Run a butter knife back and forth through the batter to swirl the added color.
Bake cake for 30-35 minutes or until an inserted toothpick comes out clean. Cool completely before frosting.