In a blender or food processor combine the watermelon and the 1/3 cup syrup. Cover and blend or process until smooth. Press mixture through a fine-mesh sieve into a medium bowl; discard pulp. Cover and refrigerate mixture at least 2 hours or up to 24 hours.
To serve, place ice cubes in ten 12-ounce glasses. Pour enough watermelon mixture into glasses to fill halfway. Add enough carbonated water to fill glasses. If desired, sweeten individual servings with additional syrup; stir to dissolve syrup.
Watermelon Ice Cubes
Cut 1-inch cubes from watermelon flesh. Place the melon cubes in a single layer in a 15x10x1-inch baking pan. Freeze for 1 to 2 hours or until firm. If storing longer than 4 hours, transfer cubes to a resealable plastic freezer bag or freezer container and freeze until ready to use. Use these cubes to keep Watermelon Cooler cold without diluting flavor.