Place cake cubes in the bottom of a trifle bowl. Stir raspberry gelatin and 1 cup boiling water together in a large measuring cup until dissolved; stir in 1 cup cold water. Pour raspberry gelatin mixture over cake cubes; press down. Spread raspberries evenly over top of gelatin; place trifle in refrigerator to chill until set, about 45 minutes.
Whisk 1 package pudding mix and 2 cups cold milk together in a bowl for 2 minutes. Spread pudding over raspberries in trifle bowl; return trifle to refrigerator to chill until pudding sets, about 45 minutes.
Stir cherry gelatin and 1 cup boiling water together in a large measuring cup until dissolved; stir in 1 cup cold water. Pour cherry gelatin over pudding in trifle bowl; spread cherries over gelatin. Return trifle to refrigerator to chill until gelatin sets, about 45 minutes.
Whisk remaining package pudding mix and 2 cups cold milk together in a bowl for 2 minutes. Spread pudding over trifle; chill until pudding sets, about 45 minutes.
Stir strawberry gelatin and 1 cup boiling water together in a large measuring cup; stir in 1 cup cold water. Pour strawberry gelatin over pudding; spread strawberries over gelatin. Return trifle to refrigerator to chill until completely set, about 1 hour.
Spread whipped topping over trifle; garnish the top with reserved berries.
