Choose whether you will make three 8-inch round cakes, two 9-inch round cakes, one 9x13-inch cake, or 24 cupcakes.
Grease and flour bottom and sides the round cake pans (and any pan you will turn the cake out of). If using a 9x13-inch pan and will be serving the cake from the pan, only grease the pan. If making cupcakes, place liners in the cupcake pans, rather than grease and flour the cups.
Cream butter and sugar together with a stand mixer (on medium speed) or with a hand mixer (on high speed) for about 2 minutes, until creamy. (If your kitchen is cold, the mixture may just be sandy. This is okay though.)
Add flour, oil, milk, baking powder, salt, and extracts. Beat for another 2 minutes, scraping down the sides partway through.
Add egg whites and whole egg. Beat for another 2 minutes. Scrape down the sides of the bowl again to be sure everything is mixed.
Pour the batter into the prepared pan(s). If making cupcakes, fill the cups no more than ½ full, or the batter will spill over.
Bake at 350F. Bake the 8-inch rounds for 23-28 minutes; 9-inch rounds for 30-35 minutes; 9x13-inch cake for 40-45 minutes; or cupcakes for 20-25 minutes. The cake will be golden brown along the top. A toothpick inserted in the middle of the cake will come out clean, not doughy or wet.
Remove cupcakes from the pan immediately. For layer cakes, let cool 10 minutes before turning the cakes out of the pans onto a cooling rack.
Let cool completely, at least an hour, before frosting.
Cake can be stored, covered, at room temperature if the frosting is shelf-stable. The cake stays soft even when stored in the refrigerator. Cake is best within 3 days, but is still delicious for a few days after that.
Notes
I use a mix of butter and oil in this recipe. Butter provides flavor, but oil cakes have a better texture when stored in the refrigerator. You can use shortening in place of the butter, but do not substitute oil, which will not give as good a texture. Shiny pans will give you a better result than dark cake pans, which will brown the edges of the cake quickly. For a 6-cup heart-shaped pan (6x3 inch), cut the ingredient quantities in half. Use 2 ½ tablespoons butter and 3 tablespoons oil, and 1 whole egg and 1 egg white. Reduce the temperature to 325F and bake for 30-45 minutes. Cool cake for 10 minutes, then turn out to a cooling rack.Adapted from the Betty Crocker CookbookAlmond flavoring suggestion from the Butternut Bakery Blog's Sweet Almond Cake, which is an all-butter cake. Calorie count calculated in MyNetDiary and is an estimate only. It assumes you're making a layer cake cut into 12 servings, and does not include frosting. 24 cupcakes would be around 158 calories each without frosting. I usually get around 20 servings out of a 9x13-inch cake.