Preheat oven to 350°F (175°C). Grease a 9-inch springform pan.
Stir together the flour, sugar, brown sugar, baking powder and salt in a large bowl. Make a well in the center of the mixture.
Place the eggs in a small bowl, and beat them lightly. Add the cooled butter, milk, and vanilla, and stir to combine. Pour into the well in the dry ingredients. Stir just until combined. Gently stir in the berries.
Transfer the batter to the prepared pan, and spread evenly. Bake 45 to 55 minutes, or until a pick inserted into the center comes out clean.
Cool the cake for about 15 minutes. Run a thin knife around the edges of the pan, and then remove the sides of the pan. Sprinkle the top with confectioners' sugar before serving.
Notes
*If you're using large berries like strawberries, I suggest chopping them into pieces about the size of raspberries.