Stir boiling water into dry gelatin in large bowl at least 2 minutes until completely dissolved. Add enough ice to cold water to measure 1 cup. Add to gelatin; stir until ice is completely melted. Let stand about 15 minutes or until thickened. (Spoon drawn through gelatin leaves definite impression.) Stir in berries.
Place cream cheese in large bowl; beat with wire whisk until creamy. Gradually add 1/4 cup of the milk, beating until well blended. Add remaining 1 cup milk and dry pudding mix; beat 2 minutes or until well blended. Gently stir in whipped topping. Set aside.
Place about half of the cake cubes in bottom of large serving bowl; cover with half of the pudding mixture. Top with layers of the gelatin mixture, remaining cake cubes and remaining pudding mixture. Refrigerate at least 1 hour or until ready to serve. Store leftover dessert in refrigerator.