Create ice cubes by filling 4 ice cube tray cavities with chopped strawberries, 4 cavities with fresh blueberries and 4 cavities with fresh mint. Fill each cavity with white grape juice and freeze overnight.
Refrigerate remaining juice and white wine overnight.
In a large pitcher, combine the remaining white grape juice, white wine and rum. Mix well. Add fruit infused ice cubes and additional (water filled) ice cubes if desired. Add remaining fresh cut berries and blueberries to the pitcher. Add about 2 tablespoons fresh mint and stir.
Fill glasses with sangria and add a fresh strawberry to the rim. Serve with a fun straw!