Preheat the oven to 350°F (177°C) and prepare six 6-inch or two 8-inch cake pans by spraying the sides with baking spray and fitting a parchment paper circle to the bottom of each pan.
In a medium bowl, add the flour, baking powder, baking soda and salt. Whisk together and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter at high speed until creamy, about 2 minutes. Add the sugar and cream it together with the butter at medium-high speed until light and fluffy, about 2 minutes, scraping the bowl and paddle at the halfway point. Turn the mixer to low and add the egg whites one at a time, mixing until they are just combined and scraping down the bowl and paddle as needed. Add the vegetable oil and vanilla, increase the mixer speed to high and beat for 1 minute.
Turn the mixer off and add the flour mixture all at once. Mix the ingredients on low speed until just combined, then slowly pour in the buttermilk. Continue mixing at low speed for about 30 seconds, until the batter is uniform and combined. The batter will be slightly thin.
Divide the batter evenly in half between two bowls. You should have about 620g of batter per bowl. Keep one half of the batter uncolored (for the white cake layers) and whisk in a few drops of red food coloring to the other half (for the red cake layers).
Divide the batter evenly between the prepared cake pans and bake. If you're using six 6-inch cake pans, you'll have about 200g per pan to create three white cake layers and three red cake layers. Bake them for 18-22 minutes, or until they spring back to the touch and a toothpick inserted comes out clean. If you're using two 8-inch cake pans, you'll add all of the white batter to one pan and all of the red batter to the other. Bake them for 30-35 minutes or until they spring back to the touch and a toothpick inserted comes out clean. Let the cakes cool in their pans for 5 minutes, then remove them from the pans and allow them to cool completely on a wire rack.