In a bowl with a potato masher mash 2 cups blackberries with 1/3 cup granulated sugar and stir in remaining blackberries. In 2 more bowls mash separately raspberries and blueberries with remaining granulated sugar in same manner. Let berries stand at room temperature 4 hours. Berry mixtures may be made 1 day ahead and chilled, covered. Bring berries to room temperature before serving.
Preheat oven to 425°F. and lightly butter 2 baking sheets. In a large bowl whisk together flour, granulated sugar, baking powder, baking soda, and salt and blend in butter until mixture resembles coarse meal. In a small bowl whisk together zest, sour cream, and milk and add to flour mixture. Stir mixture until it just forms a soft and sticky dough and drop into 12 mounds at 1-inch intervals onto prepared baking sheets. Pat dough to 1/2-inch thickness and bake 12 to 15 minutes, or until pale golden. Transfer shortcakes to a rack and cool. Shortcakes may be made 4 hours ahead and kept in airtight containers.
In a large bowl beat cream with confectioners' sugar until it holds soft peaks. Whipped cream may be made 1 hour ahead and chilled in a cheesecloth-lined large sieve set over a bowl, its surface covered with plastic wrap. Whisk cream lightly before serving.
Split shortcakes horizontally with a fork and serve with berries and whipped cream.
