Place watermelon cubes in a blender and process until completely blended. Strain half of the juice through a fine mesh sieve over a large bowl or container and discard the solids left over (you can strain the second half of juice; however, I prefer to leave some of the solids since that is the healthiest part for you). Pour watermelon juice into a large container and pour in fresh lime juice, water and ice cubes. Stir together and taste. Add more fresh lime juice if needed.