In a small saucepan, combine the sugar, water, and blackberries. Bring to a boil, smashing the berries with a wooden spoon. Boil until the syrup thickens slightly, about 3-5 minutes. Strain through a sieve if you don't want blackberry chunks.

In a pitcher, combine the limeade or lemonade and the blackberry + mint syrup. Start with 1/2 cup of the syrup, and add more to taste. Stir in vodka, if using. Serve over ice with mint and blackberries for garnish.