Add 5 cups of the watermelon cubes (save 1 cup for garnish) to a blender with the lime juice and puree until smooth. Pour into a large measuring cup. Add the Simple Syrup and mint leaves to the blender and puree until the mint leaves turn into green flecks.
Add ice to 6 glasses and then fill each glass about half full with the watermelon juice. Add a splash of the mint simple syrup to each glass. Top with sparkling water.
On each skewer, alternate the remaining watermelon cubes and mint leaves. Garnish each drink with a skewer.
Combine the sugar and 1 cup water in a small saucepan and bring to a boil. Cook, stirring, until the sugar dissolves. Remove from the heat and let cool completely. Keep covered in the refrigerator up to 1 month. Yield: 1 1/2 cups