Preheat oven to 350°F. Butter and flour a 9-inch cake pan with a removable rim (a springform pan).
In a mixer bowl, beat butter, granulated sugar, and 1 egg until mixture is pale and thickened. Beat in sour cream. Combine flour, baking powder, and soda. Beat flour mixture into butter mixture until smooth and thoroughly combined. Spread batter evenly in prepared pan.
Bake in a 350°F oven until cake is pale golden and springs back slightly when gently pressed (20 to 25 minutes).
Meanwhile, in the clean mixer bowl beat the cream cheese, powdered sugar, and remaining egg until smooth. Spread over the cake and arrange the blackberries and blueberries on top. Return the cake to the oven and bake until the edges of the topping are set and lightly browned, but the center still jiggles slightly when the pan is gently shaken (20 to 25 minutes).
Let cake cool completely on a wire rack. Then carefully loosen cake from rim and remove rim. Serve or, if making ahead, chill in an airtight container up to 1 day. Bring to room temperature to serve.