How to Make It
MAKE THE CAKE LAYERS Preheat the oven to 350°. Coat four 8-inch round cake pans with nonstick cooking spray and line with parchment paper. Dust with cake flour, tapping out the excess.
In a medium bowl, whisk the 3 cups of cake flour with the baking powder and salt. In a stand mixer fitted with a paddle, cream the butter with the granulated sugar at medium speed, scraping down the bowl as needed, until light and fluffy, about 5 minutes. Add the eggs 1 at a time, beating well after each addition. Beat in the lemon zest and vanilla. Alternately beat in the dry ingredients and milk at low speed until just combined.
Scoop 1 cup of the cake batter into each of 7 medium bowls. Using a few drops of food coloring at a time, tint the batter in each bowl to create red, orange, yellow, green, blue, indigo (dark blue-purple) and violet layers. Scrape the batter from 4 of the bowls into the prepared pans and smooth the tops with a spatula. Bake the layers for 15 minutes, until a cake tester inserted into the centers comes out clean.
Coat 3 of the cleaned cake pans with nonstick spray, line with parchment and dust with cake flour, tapping out the excess. Scrape the batter from the 3 remaining bowls into the prepared pans and smooth the tops with a spatula. Bake the layers for 15 minutes, until a cake tester inserted into the centers comes out clean. Transfer the pans to a wire rack and cool for 15 minutes. Invert each layer onto a wire rack and remove the parchment.
MAKE THE LEMON BUTTERCREAM In a stand mixer fitted with the paddle, cream the butter at medium speed until light and fluffy, about 5 minutes. At low speed, add the confectioners’ sugar in 3 batches, beating well after each addition. Add the lemon zest and salt. Beat at medium speed until smooth, about 6 minutes. Add the cream and beat until very light and fluffy, about 4 minutes.
Set the violet cake layer on a cake plate. Using an offset spatula, spread the top with 1/2 cup of the lemon buttercream. Repeat with the indigo, blue, green, yellow, orange and red layers. Spread 1 1/2 cups of the remaining buttercream over the top and sides of the cake in a thin layer. Refrigerate until the buttercream is firm, about 20 minutes. Spread the remaining buttercream on the top and sides of the cake. Decorate the top of the cake with sprinkles.