Combine the sugar and ½ cup of the water in a small saucepan. Stir to combine. Cook over medium heat, just until the sugar melts. Set aside.

In the bottom of a pitcher combine the blueberries and the mint. Using the end of a spoon or a muddler, crush the berries and the mint until pulpy and smashed. Add the juice of 4 lemons, the remaining 3 cups of water, and the reserved simple syrup. Stir to combine. Add ice to fill the pitcher and chill the lemonade.

To serve, fill a glass with ice. Pour over lemonade and additional mint and lemon slices to garnish. For an adult version, fill glass with ice and add 1 ½ ounces vodka, or to taste, and top off with lemonade, mint sprigs, and lemon slices.