Cover bottom of 8-inch square baking dish with cake cubes.
Dissolve 1 envelope of the cappuccino in ½ cup of milk; sprinkle over cake.
Beat cream cheese in a large bowl with electric mixer until smooth. Gradually beat in remaining 1½ cups milk until smooth. Add pudding mix and remaining envelope of cappuccino. Beat on low speed until blended. Stir in whipped topping.