Position a rack in the middle of an oven and preheat to 350ºF. Butter and flour 2 round cake pans each 9 inches in diameter and 1 ½ inches deep.
In a medium bowl, sift together the flour, baking powder and salt. In a large bowl, using an electric mixer set on medium-high speed, beat the butter until light. Gradually add the sugar, beating until well blended. Beat in the vanilla and almond extracts. Reduce the speed to low and, dividing the flour mixture into 3 batches, beat the flour mixture into the butter mixture alternately with the milk just until combined.
In a large bowl, using an electric mixer fitted with clean, dry beaters and set on high speed, beat the egg whites until stiff peaks form. Using a rubber spatula, gently fold the beaten whites into the batter just until incorporated. Divide the batter between the prepared pans; smooth with the spatula.
Bake until a toothpick inserted into the centers comes out clean, about 30 minutes. Transfer to racks and let cool in the pans for 10 minutes. Run a sharp knife around the pan sides to loosen the cakes. Invert onto racks and let cool completely.
Meanwhile, make the cream cheese frosting: In a large bowl, combine the cream cheese and butter. Using an electric mixer set on medium-high speed, beat until smooth. Reduce the speed to low, add the confectioners' sugar and again beat until smooth. Beat in the vanilla and almond extracts until well blended.
Using a long serrated knife, cut each cake in half horizontally. Place 1 layer on a plate. Spread ½ cup of the frosting over the top, then evenly layer with blueberries and press them into the frosting.. Top with another cake layer and evenly layer with raspberries. Top with a third cake layer and again repeat with the same amounts of frosting and blueberries. Top with the fourth cake layer, cut side down.
Spread the remaining frosting over the top and sides. Ring the top with blueberries and raspberries, and press the toasted almonds onto the sides.
Serve immediately, or cover with a cake dome and refrigerate for up to 1 day. Bring to room temperature before serving.
Makes one 9-inch cake; serves 10 to 12.
Use a white cake mix from a box if you don't want to make your own cake batter.