Preheat oven to 350 degrees and spray six 8" cake pans with non-stick cooking spray. Set aside.
Using a standing mixer, blend the butter, eggs, milk and yogurt together until incorporated. Add the dry cake mix and blend with the mixer speed on low. Scrape the sides of the bowl and mix again on medium speed until smooth.
Divide batter evenly into six large bowls and add one color of dye to each bowl. Mix thoroughly, until colors are evenly distributed. Divide batter evenly between the cake pans and evenly spread each pan of batter using a spatula. Bake 40-45 minutes, until a toothpick inserted in the center of each cake comes out clean. Cool cakes completely on a wire rack.
To make the frosting, combine the butter and yogurt together in the bowl of a standing mixer. Blend until smooth, then slowly add each frosting mix and blend together until creamy.
To assemble the cake, place the red cake on a large cake stand, then spread the top with frosting. Repeat with remaining cake layers, ending with the purple cake on top. Place 4 kabob skewers into each corners of the cake to secure it. Freeze cake 20 minutes.
Use a butter knife or spatula to frost cake completely, then garnish with rainbow sprinkles.