In a large heat-resistant bowl, mash or puree blackberries and sugar in a bowl using a fork. Set aside.
Bring 5 1/2 cups of water to a boil, and add tea bags. Cover and steep for 6-8 minutes. Then, discard tea bags.
Pour tea over blackberry and sugar mixture, and stir. Let sit for about 1 hour at room temperature. No need to cover.
Pour mixture through a wire-mesh strainer into a large pitcher. Add 3 cups of cold water. You can adjust sweetness to taste here. I don't like my iced tea to be too sweet, but if you want more sweetness, simply dissolve the preferred amount of granulated sugar with some hot water and add it to the pitcher.
Cover and refrigerate for at least 2 hours, preferably overnight.
Add lemon slices and ice cubes right before serving. Garnish with whole blackberries and mint leaves. Enjoy!