Stir together 3/4 cup hot water and 1/2 cup cappuccino drink mix in a bowl. Pour into ice cube trays, and freeze 2 hours.
Process half each of milk, sweetened condensed milk, ice cream, and cappuccino ice cubes in a blender until smooth, stopping to scrape down sides. Repeat procedure with remaining half of ingredients, and serve immediately.
Note: For testing purposes only, we used General Foods International Coffees Italian Cappuccino mix.