Preheat an oven to 350°F (180°C) with a rack set in the center. Grease desired cake pan(s) with nonstick baking spray, or line cupcake pan(s) with paper liners.
Whisk together the eggs, egg whites, milk and butter in a large bowl until smooth. Add both packages of cake mix and whisk until smooth. Pour the batter evenly into the prepared pan(s).
Bake according to the chart below; the cake is done when a toothpick inserted into the center comes out clean. Let the cake(s) cool in the pan(s) for 15 minutes, then carefully turn out onto wire rack(s) to cool completely before frosting.
Makes two 8-inch (20-cm) or 9-inch (23-cm) cakes, one 9-by-13-inch (23-by-33-cm) cake or 18 to 20 cupcakes.

To ensure a smooth batter and consistently tender cake, make sure all your ingredients are at room temperature before mixing.
Begin checking the cake(s) at the start of the time range listed to avoid overbaking.
You can make cake layers up to 2 days in advance. Once they have cooled completely, wrap them tightly in plastic wrap and keep at room temperature.

Williams Sonoma Silky Red Velvet Cake Mix