Preheat the oven to 350°F. Grease an 8-cup bundt pan with cooking spray.
In a large bowl, stir together the cake mix, eggs, water and vegetable oil.
Divide the batter evenly into six small bowls. Using the food coloring, dye each of the bowls of batter a different color.
Pour the red batter into the bundt pan, then top it with the orange, yellow, green, blue and purple.
Bake the cake until a toothpick inserted comes out clean (or according to package instructions), 33 to 36 minutes.
Remove the cake from the oven and let it cool completely before inverting onto a serving plate.
Frost the completely cooled cake then decorate with sprinkles. Slice and serve.