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Prepare cake mix as directed on package, using whole eggs. Stir in extracts. Divide batter evenly into 3 medium bowls. Stir 24 drops (about 1/4 teaspoon) yellow food color and 12 drops red food color into first bowl, tinting batter dark orange. Stir 10 drops yellow food color and 4 drops red food color into second bowl, tinting batter medium orange. Stir 5 drops yellow food color and 1 drop red food color into third bowl, tinting batter light orange.
Pour each bowl of batter into separate greased and floured 8-inch round cake pans. Bake as directed on package. Cool cakes on wire rack.
For the Frosting, beat butter and vanilla in large bowl until light and fluffy. Gradually add confectioners' sugar, beating well after each addition and scraping sides and bottom of bowl frequently. Add milk; beat until light and fluffy. Place dark orange cake layer on serving plate. Spread with 1/3 cup of frosting. Top with medium orange cake layer. Spread with 1/3 cup of frosting. Top with light orange cake layer. Frost top and sides of cake with a thin layer of frosting. Refrigerate 20 minutes.
Meanwhile, divide remaining frosting into 3 small bowls. Stir 12 drops yellow food color and 6 drops red food color into first bowl, tinting frosting dark orange. Stir 6 drops yellow food color and 3 drops red food color into second bowl, tinting frosting medium orange. Stir 3 drops yellow food color and 1 drop red food color into third bowl, tinting frosting light orange.
Frost bottom third of cake with dark orange frosting. Frost middle third of cake with medium orange frosting. Frost top third and top of cake with light orange frosting.