Mix frozen watermelon cubes, rum, lime juice, orange juice, and simple syrup in a blender until smooth. (Start with 1 tablespoon of simple syrup and add additional, to taste.) Stop to scrape the sides of the canister occasionally if not using a high speed blender.
Serve immediately, garnished with a wedge of lime.
*To make simple syrup, combine equal parts water and granulated sugar in a saucepan. (1 cup water to 1 cup sugar). Heat, stirring, until sugar is dissolved and small bubbles begin to form around the side of the pan. Remove from heat and let cool to room temperature. Store in an airtight container in the refrigerator for 3-4 weeks. Non-Alcoholic Variation:Omit rum and increase orange juice to 1/2 cup, adding a bit of water to the blender to thin the mixture, as needed.