Heat your oven to 350°F. Mix together the white cake mix, eggs, oil, and water in a large bowl, stirring just until the batter is smooth and combined without overmixing. Transfer the batter into a 9x13 inch baking pan and bake for 28 to 30 minutes, checking doneness with a toothpick inserted in the center which should come out clean. Take the pan out of the oven and allow the cake to cool completely at room temperature for approximately 30 minutes.

After the cake has cooled down, take a fork and poke holes across the entire surface to create channels for the gelatin. Mix the strawberry gelatin with 1 cup of boiling water in a bowl, stirring continuously for about 2 minutes until the gelatin is completely dissolved. Stir in the 1/2 cup of cold water to bring down the temperature slightly, then pour this mixture over the cake in a slow, even manner so it can flow into all the poked holes. Place the cake in the refrigerator for a minimum of 4 hours or overnight to allow the gelatin to set completely.

Take the softened cream cheese and place it in a mixing bowl with the sugar, then beat until the mixture becomes smooth and creamy, which should take about 2 minutes. Using a spatula, gently fold the whipped topping into the cream cheese mixture until everything is well combined and maintains a fluffy texture. Folding by hand instead of using an electric mixer helps preserve the airy consistency and prevents the whipped topping from deflating.

Take the cream cheese mixture and spread it in an even layer over the chilled cake from the previous step, making sure to cover the entire top surface. Create a flag design by placing the blueberries in a rectangular block in the upper left corner to represent the union section, then arrange the sliced strawberries in horizontal rows across the rest of the cake, leaving some white frosting rows visible between the strawberry rows to mimic the classic American flag stripes. For easier handling and to prevent the berries from sliding, chill them in the refrigerator for 30 minutes before arranging them on the frosting.

Place the finished cake in the refrigerator for at least 2 hours before serving, which allows all the layers to set properly and the flavors to blend together. This chilling period is important for achieving clean slices with the best texture. Keep the cake cold and serve it chilled.