Preheat oven to 350 degrees and spray 4 small round cake pans with nonstick cooking spray. In the bowl of a standing mixer, combine all cake ingredients. Add dry cake mixes and blend until mixture is smooth for about a minute. Divide batter evenly between 4 bowls to make the different colors.
Use natural food dye to color each bowl of cake mix to desired shade of purple. Once dyes are blended, pour into the 4 prepared pans, then bake 20-25 minutes, until a toothpick inserted in the center comes out clean. Remove from oven and cool 15 minutes in cake pans before removing cakes.
For the frosting: Blend the butter in a large bowl using an electric blender on medium-high speed. Whip 2-3 minutes, until butter becomes lighter in color and fluffy. With the blender on medium-low speed, slowly add dry frosting mix. Blend until frosting is completely incorporated into the whipped butter. Add yogurt and blend until frosting is smooth and light. Divide the frosting into two bowls. White will be used for the layers, and colored will be used for the flower on top. Use natural food dye to color frosting to desired shade of purple.
To assemble cakes: Use a sugar cookie cutter to cut out circles for the different layers of the cake. place one layer of cake onto a plate or cake platter. Evenly top with a layer of white frosting. Repeat with remaining cake layers and frosting.
For flower top: Place colored frosting in a piping bag with piping rose tip #104. Use this tip to make the rose by repeating all around the top of the cake.