1. Trim cake layers to 6-inch squares. Slice each layer in half horizontally, making a total of 4 layers. Cut a 6-inch square of cardboard or foam; set aside.

2. Microwave green ice cream until softened, about 20 seconds. Transfer ice cream to a medium mixing bowl, and stir with a rubber spatula. Place in the freezer. Microwave white ice cream until softened, about 20 seconds, and transfer to another mixing bowl. Stir with a rubber spatula.

3. Place one cake layer on the cardboard. Using an offset spatula, spread 2 cups white ice cream over the cake. Place another cake layer on top of ice cream. Place cake and bowl of white ice cream in the freezer for 20 minutes.

4. Remove the cake and the bowl of green ice cream from the freezer. Stir ice cream with the spatula to soften. With the spatula, evenly spread 2 cups green ice cream over cake. Place a third cake layer on top. Return the cake and the bowl of green ice cream to the freezer for 20 minutes more.

5. Remove the cake and the bowl of white ice cream from the freezer, and spread the remaining 2 cups white ice cream over the top; place the fourth cake layer on top of the white ice cream. Return the cake to the freezer for 20 minutes more.

6. Remove the cake and bowl of green ice cream from freezer, and spread 2 cups green ice cream over top. Return cake and ice cream to freezer, and chill the cake until firm, about 1 hour.

7. Remove the cake and remaining 2 cups green ice cream from freezer. Using a long serrated knife, trim 1/4 inch from all sides of the cake, making them even. Using an icing spatula, quickly spread the remaining green ice cream around the sides of the cake. Return the cake to freezer; freeze until completely hardened.