Preheat oven to 325°F (170°C). For 6- and 9-inch cakes: Spray 3 (6-inch) and 3 (9-inch) round cake pans with baking spray with flour. Line bottom of pans with parchment paper. For 12-inch cake: Spray a 12-inch round cake pan with baking spray with flour. Line bottom of pan with parchment paper. For sheet cake: Spray 2 (13x9-inch) baking pans with baking spray with flour. Line bottom of pans with parchment paper.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter, sugar, and oil at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add egg whites, one at a time, beating well after each addition. Beat in vanilla.

In a medium bowl, whisk together flour, baking powder, and salt. In a small bowl, whisk together milk and sour cream. With mixer on low speed, gradually add flour mixture to butter mixture alternately with milk mixture, beginning and ending with flour mixture, beating just until combined after each addition. Spoon batter into prepared pans (about 1½ cups or 327 grams each for 6-inch pans; about 3½ cups or 820 grams each for 9-inch pans; about 3½ cups or 995 grams each for sheet pans), using a small offset spatula to smooth tops. Firmly tap pans on a kitchen towel-lined counter 3 to 4 times to settle batter and release any air bubbles.

Bake until golden brown and a wooden pick inserted in center comes out clean, 30 to 35 minutes for 6-inch layers, 45 to 50 minutes for 9-inch layers, 45 to 50 minutes for 12-inch cake, and 30 to 35 minutes for sheet cakes. Let cool in pans for 10 minutes. Remove from pans, and let cool completely on wire racks.

Level cooled cake layers for flat top. (If preparing ahead of time, wrap each cake layer separately in plastic wrap, and freeze until ready to use. Let thaw overnight in refrigerator before using.)