Preheat oven to 325°F. Grease and flour a bundt pan.
Prepare the white cake mix according to package directions. Pour the prepared batter into a large mixing bowl so you can measure and divide it.
Spoon 1 1/3 cups batter evenly into the prepared bundt pan. Place 2 tablespoons batter in a small bowl and set it aside (reserved white batter).
Divide the remaining batter into six bowls as follows: 2 tablespoons into bowl A, 1/4 cup into bowl B, 1/3 cup into bowl C, 1/2 cup into bowl D, 2/3 cup into bowl E, and all remaining batter into bowl F.
Tint each bowl with the paste food colorings listed: tint bowl A purple (or purple/blue), bowl B blue (or purple/blue), bowl C green, bowl D yellow, bowl E orange, and bowl F red. Stir each bowl until the color is even.
Spread the red batter (bowl F) in a wide ring on top of the white batter in the pan, leaving about 1/2 inch of the pan edge and some white batter visible around the outside.
Working inward, spread the orange batter (bowl E) in a ring inside the red ring, leaving some red visible on both sides. Continue layering inward in this order so each ring is narrower than the last: yellow (bowl D), green (bowl C), blue (bowl B), and purple (bowl A) as the innermost colored ring.
Spoon the reserved 2 tablespoons of white batter over the purple ring only, spreading gently to cover that center area.
Bake 40–45 minutes, or until a toothpick inserted in the center comes out clean. Cool completely in the pan on a wire rack, then invert the pan to release the cake onto a serving plate.
In a medium bowl, beat 1 cup heavy whipping cream until it begins to thicken. Add 3 tablespoons powdered sugar and 1/2 teaspoon vanilla extract and continue beating until stiff peaks form. Serve cake slices with the whipped cream as "clouds."