Preheat the oven to 350°F. Grease and flour the cake pans.
Cut three rounds of parchment paper and place them flat in the bottom of the cake pans. (You can use the bottom of a pan to trace a circle.)
Sift the flour, baking soda, baking powder, and salt in a large mixing bowl. Whisk to combine. Set aside.
In a mixing bowl, cream the butter and sugar with a mixer until light and fluffy, about 2 minutes. Scrape down the sides, ensuring the butter and sugar are well combined.
Add the eggs and egg whites one at a time, beating after each addition, just until combined.
Stir in the vanilla bean paste and extract.
Stir together the buttermilk and sour cream. Then, alternate adding the flour and buttermilk mixture, beginning and ending with flour, incorporating a little of each at a time while beating between additions. Be careful not to overbeat the batter.
Divide the batter evenly among the three pans. To promote even cooking and ensure the cakes are flat, use baking strips (see the note below for an easy alternative).
Bake for 28 minutes or until a toothpick inserted into the center of the cake comes out clean or with crumbs. (If using baking strips, you may need to add extra minutes to the cooking time.) Cool on racks for a few minutes. Then remove the cakes from the pans and lift the parchment paper from the bottom of each cake. Cool completely before frosting.