Pre-heat oven to 350°F.
Spray three 9-inch round cake pans with baking spray.
In a large bowl, with an electric mixer at low speed, blend cake mix, water, eggs, oil and vanilla until moistened; continue to beat, at medium speed, for 2 additional minutes.
Divide batter evenly into 6 bowls, about 1 1/2 cups each; add 1/2 teaspoon red food coloring to one bowl, 1/4 teaspoon yellow to another and 1/4 teaspoon orange to a third bowl of batter; stir each until blended.
Pour each into separate pans; place in pre-heated oven and bake 14 to 16 minutes, until toothpick comes out clean; cool 10 minutes; remove from pans to cooling racks and cool completely.
Meanwhile, add 1/2 teaspoon blue food coloring to one of the remaining bowls of batter, 1/2 teaspoon green to another and 1/2 teaspoon purple to the final bowl; stir until blended. refrigerate until ready to bake.
Wash, dry and spray cake pans with baking spray; pour each remaining color into separate pans and bake 14 to 16 minutes, until toothpick comes out clean; cool 10 minutes; remove from pans to cooling racks and cool completely.