Line up several 3 oz. paper cups on a sheet pan. Pour 2 tablespoons of red juice into each cup. Freeze 2-3 hours until firm-slushy.
Remove from freezer and poke a popsicle stick into the center of each cup of juice. Add 2 tablespoons of white juice and freeze 2-3 hours.
Remove from freezer. Top off with blue juice and freeze 1-2 hours until slushy.
Remove from freezer and insert a 2 or 3-inch string of licorice into each popsicle. Freeze until hard. Peel off paper cups to serve.