Special equipment: a small offset spatula; 2 piping bags fitted with large star tips and 2 piping bags fitted with large round tips
Combine 1 package cream cheese, 2/3 cup of the confectioners' sugar and 1 tablespoon of the vanilla extract in the bowl of a stand mixer fitted with the whisk attachment and whip on medium until light and airy, about 2 minutes. Turn the mixer speed to low and stream in 1 quart heavy cream. Mix until incorporated; scrape the sides then increase the mixer speed to high and whip to stiff peaks, 4 to 5 minutes. Transfer to a large bowl and repeat with the remaining cream cheese, sugar, vanilla and cream. Add the mixture to the large bowl.
Transfer 1/2 cup of the cream mixture to a small bowl and color it with 4 drops of the blue food coloring. Transfer 1 1/4 cups of the cream mixture to a medium bowl and color it with 8 drops of the red food coloring. Transfer 1 3/4 cups of the cream mixture to a second medium bowl (do not color it). Cover all 4 bowls and refrigerate while you assemble the cake.
Split the angel food cakes in half horizontally using a long, serrated knife. Keeping the layers stacked, cut each cake in half vertically. Arrange 2 of the stacked halves from one cake on a large platter or cake board so that they create an S shape; slide the ends so they are slightly offset. Repeat with the second cake, nestling the halves up against those of the first cake so that together they resemble a thick curved line. (There will be some gaps between the cakes.) Repeat with the third cake.
Trim the edges of the arches along the short ends of the cake to create a more or less straight line (these will be the ends of the flag). Use half of the cake scraps to fill in the holes between the cake stacks. Reserve the other half of the scraps.
Remove the top pieces from the cake stacks and set them aside. Spread the bottom pieces with 3 cups of the undyed cream mixture in the large bowl. Scatter the strawberries and blueberries on top. Dollop with 3 more cups of the cream mixture and spread it evenly. Top with the reserved top cake pieces. Fill in the gaps between the cake stacks with the remaining cake scraps. Cover the sides and the top of the cake with the remaining cream mixture in the large bowl.
Transfer the blue cream mixture and 1/2 cup of the reserved white cream mixture (from the medium bowl) to separate pastry bags fitted with large star tips. Transfer the red cream mixture and the remainder of the reserved white cream mixture (from the medium bowl) to separate pastry bags fitted with large round tips.
For the stars: Pipe a blue star in the upper left corner of the cake; use a small offset spatula to press down in the center of the star and then drag the spatula to the right to create a short smear. Wipe the spatula clean. Pipe a white star next to the blue one and repeat the pressing and dragging motion; wipe the spatula clean. Repeat piping and dragging stars in alternating colors, wiping the spatula clean between each, to make 3 rows of stars in the upper left corner of the cake.
For the stripes: Use the same piping and dragging technique to create red and white stripes, but pipe dots with the pastry bags fitted with the round tips instead of the ones with stars.
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