Step 1
Preheat the oven to 350 degrees F (175 degrees C). Grease the sides of three 9-inch round cake pans; line bottoms with parchment paper.
Step 2
Beat butter with sugar in a large bowl using an electric mixer until fluffy. Add eggs 1 at a time beating well after each. Mix in vanilla extract. Combine flour baking powder and baking soda. Stir into butter mixture alternately with buttermilk making 3 additions of flour mixture and 2 of buttermilk.
Step 3
Divide batter among 3 bowls. Tint one bowl red one yellow and one blue. Scrape each into one of the prepared pans and smooth the tops.
Step 4
Bake in the preheated oven until a toothpick inserted into the centers comes out clean about 30 minutes. Cool cakes on a wire rack for 15 minutes. Run a table knife around the edges to loosen. Turn out onto a cooling rack. Peel off parchment paper and let cool for 30 minutes before frosting.
Step 5
Beat unsalted butter and salt together in a large bowl until smooth. Beat in confectioners' sugar alternately with cream making 3 additions of sugar and 2 of cream. Mix in vanilla extract. Divide butter icing among 3 bowls. Tint one orange one green and the other purple.
Step 6
Place red cake layer on flat serving plate; spread top with orange icing. Top with yellow layer; spread green icing on top. Add the blue layer and cover it with purple icing. Refrigerate for 30 minutes or until icing is firm.
Step 7
Place corn syrup in a saucepan and bring to a boil. Meanwhile beat egg whites and cream of tartar together until frothy in a heat-proof bowl set over a pan of simmering water. Beat in the corn syrup in a thin steady stream until stiff peaks form. Remove from heat and beat in vanilla. Top cake with fluffy icing.