In large bowl, combine strawberries, 1 cup raspberries and blackberries. Sprinkle with 1/4 cup sugar and 2 tablespoons liqueur; stir until all berries are coated. Cover; refrigerate at least 3 hours.
Meanwhile, heat oven to 400ºF. Line air-cushioned baking sheet with parchment paper, or place 2 baking sheets together and line top sheet with parchment paper. (This helps control overbrowning the bottoms of these shortcakes.) In another large bowl, combine cake flour, all-purpose flour, 1/2 cup of the sugar, cocoa, baking powder, baking soda, cream of tartar, salt and espresso coffee powder; mix well.
Add butter. Using pastry blender or 2 knives, cut in butter until mixture resembles coarse crumbs with pea-size pieces of butter. Add buttermilk, 3/4 teaspoon vanilla and egg; stir until dough forms.
Sprinkle work surface lightly with cake flour. Turn out dough onto flour. (Dough will be sticky.) With floured hands, gently knead 12 to 14 strokes. Pat dough into round 1 inch thick.
Cut out shortcakes with floured 2 1/2-inch round cutter, pressing dough scraps together when necessary. Place on baking sheet; sprinkle tops with remaining 2 teaspoons sugar.
Bake 14 to 16 minutes or until shortcakes are firm to the touch. Cool on wire rack at least 20 minutes.
Meanwhile, in food processor, combine raspberries with their syrup and 2 tablespoons liqueur; puree until smooth. Place strainer over medium bowl; pour raspberry mixture into strainer. Press mixture with back of spoon through strainer to remove seeds; discard seeds. Cover; refrigerate until serving time.
In large bowl, whip cream, sour cream, 2 tablespoons sugar and 3/4 teaspoon vanilla at medium-high speed until soft peaks form. Cover; refrigerate until serving time.
To serve, split shortcakes in half horizontally. Place bottom halves on individual dessert plates. Top with cream and berries. Cover with shortcake tops. Pour some raspberry sauce onto plates around shortcakes. Serve with remaining sauce. Refrigerate leftovers.