Prepare, bake and cool the white cake as directed for 8" layers. Make sure it's completely cooled before slicing.
Using a long, serrated knife, slice the layers in half horizontally. Place one layer, cut side up, in the bottom of an 8" springform pan. Attach sides of pan.
Spoon the softened lime sherbet over the first cake layer. Top with second cake layer, spread with orange sherbet. Top with third layer and spread with raspberry sherbet. Top with final cake layer, cut side down. Cover with plastic wrap and freeze for 3-4 hours.
For frosting, in a large bowl, mix cream cheese, powdered sugar, vanilla and milk on med/high speed until light and fluffy. Fold in Cool Whip.
Remove cake from springform pan and move to cake plate. Spread top and sides with frosting, add sprinkles and freeze, uncovered for 1-2 hours or until firm.
Let stand at room temperature for 10-15 minutes before slicing.
To make it easier to slice the cake layers, freeze them for a bit after cooling.
Use toothpicks inserted in each side to help keep the knife blade centered.
Make sure the sherbet is very soft for spreading, but not melted, or it will make the cake layers soggy.
Press down gently on the top layer of the cake to help seal in the ice cream layers.
Dip a knife in hot water to get clean slices of cake for serving.