Preheat oven to 350 degrees F.
Spray a 9-inch by 13-inch cake pan with non-stick baking spray. Set aside for now.
Split the dry cake mix evenly into 3 separate medium-sized bowls (125 grams of dry cake mix per bowl).
In the first bowl, combine 125 grams of the dry cake mix, vanilla ice cream, 1 egg and 1/3 of the vegetable oil (1 tablespoon + 1 teaspoon = 20 ml). Using an electric mixer, beat on medium speed for 1 minute until combined well. Use a spatula to scrape down the sides of the bowl.
In the second bowl, combine 125 grams of the dry cake mix, strawberry ice cream, 1 egg, 1/3 of the vegetable oil (1 tablespoon + 1 teaspoon = 20 ml), strawberry flavor and 1 drop of pink food coloring. Using an electric mixer, beat on medium speed for 1 minute until combined well. Use a spatula to scrape down the sides of the bowl. The amount of food coloring you use depends on how bright you want the pink cake batter to be.
In the third bowl, combine 125 grams of the dry cake mix, chocolate ice cream, 1 egg, 1/3 of the vegetable oil (1 tablespoon + 1 teaspoon = 20 ml) and cocoa powder. Using an electric mixer, beat on medium speed for 1 minute until combined well. Use a spatula to scrape down the sides of the bowl.
Using 3 separate spoons (1 spoon per cake batter), drop spoonfuls of batter into the prepared cake pan in a random pattern alternating between the 3 different colors of cake batter. These spoonfuls should be small enough that when you cut slices of the baked cake you’ll have some vanilla, strawberry and chocolate cake in each piece.
To smooth out the batter before baking, give the bottom of the filled cake pan a few light taps on the counter to settle the batter into an even level.
Bake for 30 to 32 minutes or until a toothpick inserted into the middle comes out clean.
Let the cake cool completely before adding frosting.