Prepare batter according to package directions. Pour into two round cake pans and drop a few tablespoons of jam on top. With a butter knife, swirl the jam into the cake. Bake according to package directions. remove from oven and let cool.
Line another cake pan with plastic wrap and fill it with ice cream. Place into the freezer to harden.
To assemble the cake. slice each cake in half through the middle. Remove the ice cream from plastic wrap and slice it in half. Build the cake by layering cake and then ice cream. With the extra fourth layer of cake, crumble it into a bowl and reserve.
Frost cake with cream cheese frosting. Coat the sides of the cake with the crumbled pieces of cake and garnish the top with strawberries.