Preheat oven to 350 degrees F (175 degrees C). Line 2 muffin tins with cupcake liners.
Combine cake mix, Champagne, egg whites, whipped topping mix, vegetable oil, egg, and red food coloring in a large bowl; beat with an electric mixer on low speed until smooth, about 3 minutes. Pour batter into lined muffin tins.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 17 to 20 minutes.