Place 24 watermelon cubes on a baking sheet lined with parchment. Cover, and freeze at least 1 hour (up to 2 days).
Puree remaining watermelon and the sugar in a blender until smooth. Pass through a sieve lined with cheesecloth into a bowl. (You should have 3 cups.)
Place tequila and basil in a glass pitcher, and crush with a wooden spoon. Stir in watermelon juice and triple sec.
Place watermelon cubes in glasses. Using a cocktail shaker, mix 3/4 cup margarita with 1 cup ice. Strain into a glass. Repeat. Serve garnished with basil.