Butter the bottom of a 13 by 9 by 2-inch pan. Line with whole graham crackers. In bowl of an electric mixer, mix pudding with milk; beat at medium speed for 2 minutes. Fold in whipped topping. Pour half the pudding mixture over graham crackers. Place another layer of whole graham crackers on top of pudding layer. Pour over remaining half of pudding mixture and cover with another layer of graham crackers.
For frosting, blend together sugar and cocoa. Add butter and milk, mixing well. Add corn syrup and vanilla. Stir until creamy. Cover cake with frosting and refrigerate for 24 hours.