Cream butter and sugar in a large bowl. Add eggs, one at a time, beating well after each addition. Add vanilla, milk, and sour cream. Beat well.
Sift in cake mix; beat on low speed until incorporated. Sift in cake flour; beat on low speed until incorporated. Finish folding ingredients with a wooden spoon or rubber spatula to ensure that all ingredients are well combined.
Divide the batter into thirds, roughly 16 ounces each. Color one orange, one green, and one purple to the desired color with gel food coloring. (See Note 7)
Preheat oven to 350°F. Thoroughly grease a 10- to 12-cup Bundt pan, or spray with nonstick baking spray.
Spoon a layer of orange, green, purple, orange, green, and purple batter into the bottom of a bundt pan. Carefully swirl with a butter knife. Tap the pan several times on the counter to evenly distribute.
Repeat the first layer beginning where the purple and green meet on the bottom layer. Swirl with a toothpick. Tap to evenly distribute. Repeat again for the third layer.
Bake at 350° F for 50 to 55 minutes, or until a toothpick inserted into the center comes out clean.
Remove from oven; let the cake cool in the pan for 10 minutes. Invert the cake on a wire rack; cool completely.