Combine sugar and 1 cup water together in a saucepan; bring to a boil for 3 minutes. Remove saucepan from heat and stir in strawberry drink mix. Pour strawberry drink into a large stockpot and stir in pineapple juice, lemonade concentrate, lemon-lime soda, and 4 cups water. Pour mixture into a large freezer-safe container and freeze until solid, at least 4 hours.
Remove container from freezer and allow to thaw slightly, about 15 minutes. Break mixture apart with a spoon and place in a punch bowl and stir in lemon-lime soda.