Place half of cake cubes in bottom of an 8-inch square baking dish. Set aside. Combine mocha-flavored cappuccino mix and 1/2 cup milk in a small microwave-safe dish. Micro-wave at HIGH 35 seconds, stirring until mix dissolves. Set aside.
Beat cream cheese with a mixer at medium speed until smooth. Add 1 cup milk; beat until smooth. Add pudding mix; beat until blended. Combine vanilla-flavored cappuccino mix and remaining 1/2 cup milk in a small microwave-safe dish. Microwave at HIGH 35 seconds, stirring until mix dissolves. Add vanilla cappuccino mixture to cream cheese mixture. Fold in whipped topping.
Pour half of mocha cappuccino mixture over cake; top with half of cream cheese mixture. Place remaining cake cubes on top of cream cheese mixture, and drizzle with remaining mocha cappuccino mixture. Top with remaining cream cheese mixture. Sprinkle with grated chocolate, if desired. Cover and chill, or serve immediately.