Using lime wedges, moisten the rim of six glasses. Set limes aside for garnish. Sprinkle 3 tablespoons sugar on a plate; hold each glass upside down and dip rim into sugar. Set aside. Discard remaining sugar on plate.
In a blender, combine the water, limeade concentrate, strawberries, ice cubes and remaining sugar; cover and blend until smooth. Pour into prepared glasses. Garnish with reserved limes. Serve immediately.