If you want to make the Big Red flavor stronger in the icing, try reducing it into a syrup ahead of time. Simmer 3 cups Big Red over medium high heat for about 25 to 30 minutes. You should end up with about 1/2 cup Big Red syrup that you could use in place of Big Red for the icing. It'll need to cool completely before making the icing. Keep in mind, though, that because cooking it neutralizes the carbonation, this wouldn't be good to put in the cake itself.