Divide ice cream into thirds. Place into individual bowls to soften to a spreadable consistency while you continue with next steps.
Tear cake into small pieces. Divide into thirds and place each third into a medium size bowl. Sprinkle one flavor of dry gelatin over each cake portion. Toss lightly with fork until cake is well-coated.
Place strawberries cake pieces in bottom of a 10 inch tube pan. Sprinkle any excess gelatin over cake. Spoon strawberries over cake. Spread one third of the ice cream over the strawberries.
Repeat layers with lime cake pieces, crushed pineapple, ice cream, orange cake pieces, oranges and ice cream.
Freeze until firm, preferably a day or so, so that the gelatin blends into the cake pieces.
Unmold on a chilled plate and cut into wedges to serve.