Glorious Red, White, and Blue Cake

INGREDIENTS

• 1/3 cup vegetable oil
• 1 pint (12 ounces) blueberries
• 3 1/4 cups confectioners' sugar
• 1 stick (1/2 cup) unsalted butter, softened
• 1 1/2 teaspoons white or cider vinegar
• 2 large eggs
• 1 (1-ounce) bottle (2 tablespoons) red food coloring
• 2 1/2 tablespoons fresh lemon juice
• 3/4 cup granulated sugar
• 2 1/2 cups sifted cake flour, not self-rising (sift before measuring)
• 3 large egg whites
• 1 1/3 cups sifted cake flour, not self-rising (sift before measuring)
• 1/4 cup sour cream mixed with 2 tablespoons water
• 1 pint (8 ounces) strawberries, preferably small; halve or quarter if large
• 5 tablespoons unsalted butter, softened
• 1 1/2 teaspoons vanilla extract
• 2 1/2 (8-ounce) packages cream cheese (20 ounces total), softened
• 1 teaspoon baking soda
• 1/4 cup unsweetened natural cocoa (such as Hershey's; not Dutch process or extra-dark cocoa)
• 2 teaspoons vanilla extract
• 1 tablespoon grated lemon zest (best done with Microplane zester or grater)
• 2 1/2 sticks (1 1/4 cups) unsalted butter, softened
• 1/2 pint (6 ounces) blackberries
• 1 cup vegetable oil
• 1 1/2 cups granulated sugar
• 1 teaspoon vanilla extract
• 3/4 cup sour cream mixed with 1/4 cup water
• 3/4 teaspoon salt
• 1/2 teaspoon baking soda
• 1/4 teaspoon salt