Preheat the oven to 350°F. Spray a Bundt pan with baking spray and set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl if using a hand mixer), cream 6 tablespoons unsalted sweet cream butter and 1 cup granulated sugar on medium speed until light and fluffy.
With the mixer on low, add the 4 large egg whites one at a time, mixing until each is incorporated.
Add 2 teaspoons pure vanilla extract and 1 teaspoon pure almond extract and mix briefly to combine.
In a separate bowl, whisk together 2 cups all-purpose flour, 2 teaspoons baking powder and 1/4 teaspoon kosher salt.
Add the flour mixture to the butter mixture in two additions, alternating with 2/3 cup milk: add half the flour mixture and mix on low until just combined, add the milk and mix to combine, then add the remaining flour mixture and mix on low until there are no large streaks of flour.
Increase the mixer speed to high and beat the batter for 1 minute to finish.
Divide the batter into three equal portions.
Color one portion with red food coloring to your desired shade; color a second portion with blue food coloring to your desired shade; leave the third portion uncolored (white). Stir each portion until the color is evenly distributed.
Pour the colored batters into the prepared Bundt pan in layers: first the red, then the white, then the blue. Pour gently and do not attempt to smooth or swirl the layers — they should remain mostly separated.
Bake the cake at 350°F for 30–36 minutes, or until a toothpick or cake tester inserted into the center comes out clean.
As soon as the cake tests clean, remove it from the oven and let it rest in the pan for 2 minutes.
Invert the pan onto a cooling rack, release the cake from the pan, then transfer the cake to a wire rack. Let the cake cool completely before icing.
For the icing: in the bowl of a stand mixer, beat 2 sticks butter and 1 (8 oz) block cream cheese (both at room temperature) together until smooth.
Add 4 cups powdered sugar, 2 teaspoons pure vanilla extract and 1 teaspoon pure almond extract. Mix on low until the sugar is incorporated, then increase speed and beat until the icing is smooth.
Divide the icing into three equal portions.
Color one icing portion red and one portion blue to your desired shades; leave the third portion white. Stir each portion until the color is even.
Microwave each colored icing portion in short intervals (about 30 seconds to 1 minute total, checking and stirring after short bursts) until it is slightly runny and drizzleable.
Using a large spoon, drizzle the red, white and blue icings over the cooled cake, moving the spoon back and forth to create stringy layers across the top.