Place watermelon cubes in a single layer in an extra-large zip-top plastic freezer bag and freeze 8 hours.
When ready to prepare, remove cubes from freezer, let stand at room temperature 15 minutes.
Process half each of watermelon, gingerale, water, and limeade concentrate in a blender until smooth; pour mixture into a pitcher. Repeat procedure with remaining half of ingredients; stir into the pitcher, and serve immediately.