Preheat oven to 350 degrees F.
In a large bowl, beat the butter and sugar until creamy and light, about 2-3 minutes. Add oil and beat again, scraping down the bottom and sides of the bowl.
In a separate bowl, whisk the egg whites, vanilla extract, almond extract, and milk together. Set aside.
Add 1 cup of the flour with the baking powder, baking soda, and salt to the creamed butter and sugar mixture. Mix well, then add about half of the milk and egg white mixture, beating again. Add another cup of the flour, followed by the remaining liquid and final cup of flour, mixing and scraping the bowl between each addition.
Transfer 1 and ¼ cups of the batter to one bowl and add red food coloring. Do the same thing with another 1 and ¼ cups of the batter in another bowl with the blue food coloring. Stir well to evenly color the batter. Transfer the two batter colors to piping bags or ziploc bags with the tip snipped off.
Spray your bundt pan with baking spray. Pipe some of the red batter into alternating sections of the pan. Repeat with the blue batter to fill in the empty sections. You can use a skewer to nudge the batter into the corners and edges, if needed.
Spoon some of the white batter into the bundt pan, then add more of the red and blue batters, followed by the remaining white batter until it has all been used up. You can gently swirl the batter with a knife or just leave it be. As it bakes, the colors will swirl themselves pretty well anyway.
Bake for 50-60 minutes until a toothpick inserted into the center of the cake comes out clean with just a few crumbs. Cool for 10-15 minutes in the pan before turning the cake out onto a wire rack to cool completely. I like to slice off the bottom (top?) of the cake so that it will set level on a cake stand for better presentation.
Once the cake has cooled completely, make the marshmallow icing by beating the marshmallow cream in a bowl with the powdered sugar and heavy cream until smooth and thin enough to pour. Pour the icing over the ridges of the cake, letting it run down the sides. Sprinkle with patriotic sprinkles, then slice and serve.