Preheat oven to 350°F. Line three 9-inch cake pans with circles of parchment paper on the bottom and spray the sides with baking spray.
Whisk the flour, baking powder, baking soda, and salt together in a large bowl. Set aside.
3 3/4 cups cake flour, 2 teaspoons baking powder, 1/2 teaspoon baking soda, 1 teaspoon salt
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter and shortening on high speed for 1 minute until smooth and creamy. With the mixer running on low speed, add the sugar, then increase the speed and beat on high speed for 5 minutes until light. Scrape the sides of the bowl using a rubber spatula.
1 cup butter, 1/2 cup shortening, 2 cups granulated sugar
Add eggs and egg whites one at a time, beating well after each addition. Add in the vanilla extract and scrape the sides of the bowl again.
4 large eggs, 2 egg whites, 3 teaspoons vanilla extract
Add the dry ingredients alternately with the buttermilk in 2-3 additions, mixing just until incorporated. Do not overmix.
1 1/2 cups buttermilk
Add the sprinkles and use a spatula to gently fold the sprinkles into the batter. Divide batter evenly between the prepared cake pans.
3/4 cup rainbow sprinkles
Bake for 25-28 minutes or until the cakes are baked through. To test for doneness, insert a toothpick or sharp knife into the center of each layer. It should come out clean or with just a few moist crumbs if the cake is done.
Let the cakes cool for 5-10 minutes in the pans before turning them out onto wire racks to cool completely. Do not try to assemble and frost the layer cake before the layers are completely cool.