Double Rainbow Happiness Cake

Work: 1 hour 30 minutes
Total: 2 hours 40 minutes

3 boxes white cake mix, batter prepared
Gel paste food coloring
8 large egg whites
2 cups sugar
6 sticks unsalted butter, softened
1 1/2 teaspoons vanilla extract
1/3 cup apricot jam
1/4 cup white sprinkles

1. Heat oven to 350 degrees F. Grease two 9-by-5-inch straight-sided loaf pans and line bottoms with parchment. Pour 1 rounded cup cake batter into each of 7 bowls and color with food coloring. We made fuchsia, light pink, peach, purple, yellow, green, and turquoise.
2. Pour two batters into prepared loaf pans. Bake for 15 minutes, until cooked through. Allow cakes to cool slightly, remove cake, wipe pans clean, and repeat with remaining batter.
3. For buttercream frosting, whisk egg whites and sugar in a heatproof bowl over a pan of simmering water until sugar is dissolved, about 5 minutes. Remove from heat; beat on high speed until stiff peaks form, 6 to 10 minutes. Reduce speed and add butter a few tablespoons at a time until incorporated. Add vanilla and stir until smooth.
4. Trim domed tops from cakes and place one cake on a serving platter. Combine apricot jam with 3 cups buttercream and spread about 1/2 cup onto each layer. Smooth a thin layer (a "crumb" coating) of the remaining buttercream all over the cake and chill for 20 minutes. Frost again with a final coat of buttercream and top with sprinkles. Serves 14.