Preheat oven to 350°F / 175°C. Line four 8" round cake pans with parchment rounds and grease with non-stick baking spray or
homemade cake pan release.
Mix 3 cups all-purpose flour, 3 cups sugar, 2 1/2 tsp baking powder, and 1 tsp salt together in a stand mixer with a paddle attachment or hand mixer until fully combined.
Mix in 1 cup of room temperature, unsalted butter slowly into the dry ingredients on a low speed. Continue to mix until no large chunks of butter remain, and the mixture looks like moist sand.
Pour in 1 cup of egg whites and mix on low until just incorporated. Scrape the sides and bottom of the bowl as needed with a rubber spatula.
Then mix in 1 1/2 cups sour cream, 2 Tbsp of vegetable oil, and 1 Tbsp of vanilla on a low speed until fully incorporated.
Scrape down the sides of the bowl with a rubber spatula one more time, then beat on a medium speed for about 30 seconds to make sure everything is properly mixed together. This also helps lighten the texture of the cake layers.
Divide the batter evenly between four bowls (about 450 grams of batter per bowl). Create blue, purple, pink, and yellow batter using a squirt of gel food coloring. Mix by hand with a spatula until the batter is evenly colored.
Pour each color into one of the prepared cake pans. Bake for 31-35 minutes or until a toothpick comes out clean. Let the pans cool for 10 minutes, then run an offset spatula around the perimeter of the pan to separate the cake from the pan.
Place cake layers into the freezer for 45 minutes to accelerate the cooling process. Once the layers are fully cooled, carefully flip the pans, and remove the layers from the pans.
Use a serrated knife to level the tops of the layers. Then use a 6", 4" and 2" circle cutter to carefully cut each layer into four rings. If you don’t have circle cutters those sizes, make a 6”, 4”, and 2” template with
parchment paper and cut the layers with a small, sharp knife. Carefully reassemble the layers, following the same color pattern (blue, purple, pink, yellow). Set aside.
If you make these cake layers in advance and freeze them, let them thaw for about 20 minutes before making the cake. The cake layers should still be slightly cold to the touch, which will make it easier to assemble the cake.