Begin by making the blue layer: Put 1 1/2 cups of the ice cubes in the carafe of a blender. Add the passion fruit liqueur, lime juice, blue curacao, rum and sugar. Blend until slushy and there are no chunks of ice left, adding the remaining 1/2 cup of ice if needed. Transfer to a large measuring cup or small bowl and place in the freezer while you make the next layer.

For the red layer: Rinse out the blender and then add the frozen strawberries, watermelon, lime juice, rum and sugar. Blend until slushy and there are no chunks of fruit. With the motor running, add the ice, a few cubes a time, until thick and smooth. Stir in 1 to 2 tablespoons water if the consistency is too thick. Transfer to another small bowl and place in the freezer while making the final layer.

For the white layer: Rinse out the blender and add the coconut sorbet, rum and lime juice. Blend until smooth and thick. With the motor running, add the ice, a few cubes at a time, and continue to blend until thick and no bits of ice remain.

Pour the red layer into the bottom of six 8-ounce glasses, about 1/3 cup each. Gently spoon 1/3 cup of the blue layer over the red layer so they stay separate. Finish by spooning 1/3 cup of the white layer over the second layer in each glass.