In a saucepan, heat the sugar and 1/4 cup water over medium, stirring, until the sugar dissolves. Let cool. In a pitcher, stir the sugar syrup, melon liqueur, vodka and lime juice.
Make 2 drinks at a time: Blend 1 cup Sour Melon Ball mix, 2 cups honeydew and 1 1/2 cups ice. Garnish drinks with lime wedges and mint sprigs. Repeat!