Begin by making the red layer: Put the frozen strawberries, watermelon, lime juice, rum, sugar and ice in the carafe of a blender. Blend until thick and smooth. Stir in 1 to 2 tablespoons water if the consistency is too thick. Transfer to a large measuring cup or small bowl and place in the freezer while you make the next layer.
For the white layer: Rinse out the blender and add the coconut sorbet, rum, lime juice and ice. Blend until thick and smooth. Transfer to another large measuring cup or small bowl and place in the freezer while you make the final layer.
For the blue layer: Rinse out the blender and add the passion fruit liqueur, lime juice, blue curacao, rum, sugar and ice cubes. Blend until slushy and there are no chunks of ice left.
Pour the red layer into the bottom of six 8-ounce glasses, about 1/3 cup each. Gently spoon 1/3 cup of the white layer over the red layer so they stay separate. Finish by spooning 1/3 cup of the blue layer over the second layer in each glass.