Preheat the oven to the temperature on the back of the cake box. Prepare and grease the cake pans. Set aside.
In a large bowl, combine the cake mix, water, vegetable oil, sour cream, and eggs. Mix well to combine.
Evenly distribute the batter into six bowls to make all of the colors. Add the desired amount of food coloring to each bowl and mix until the color is smooth.
Add the batter to the pan for each color and bake according to the package on the back of the cake mix box.
Let the cake cool completely before frosting the cake with buttercream frosting. Frost the cake, first with a crumb coat, and then with the remaining frosting. Top with sprinkles if desired.