Preheat oven to 350℉.
In the bowl of a stand mixer, or in a large bowl, beat the butter and sugar on medium speed untill it is light and fluffy, about 2 minutes. Add the oil and beat until incorporated. Scrape down the sides of the bowl with a rubber spatula.
1 cup unsalted butter, 2 cups granulated sugar, ½ cup vegetable oil
In a medium bowl, whisk the egg whites, milk, vanilla and almond extracts. Set aside.
6 egg whites, ¾ cup milk, 1 tbsp pure vanilla extract, ¼ tsp almond extract
In the mixer bowl, add the baking powder, baking soda, salt and 1 cup of the flour. Mix on a low speed just until incorporated. Then add half the egg mixture and mix on low until incorporated. Add 1 cup of flour, mix just until incorporated. Add the rest of the egg mixture and mix until incorporated. Add the final 1 cup of flour and mix just until incorporated. Use a rubber spatula to scrape down the sides of the bowl and mix on low for a few seconds until evenly incorporated.
1 ½ tsp baking powder, ½ tsp baking soda, 1 ½ tsp salt, 3 cups all-purpose flour
Use a liquid measuring cup to transfer 1 ¼ cups of batter into a small bowl. Add the raspberry emulsion and a toothpick of red gel food coloring. Mix well with a spoon until the color is evenly distributed. In a second bowl, transfer another 1 ¼ cups of the white batter. Add the blueberry emulsion and a toothpick of the blue gel food coloring. Mix until the color is evenly distributed.
½ tsp raspberry emulsion, ½ tsp blueberry emulsion, red gel food coloring, blue gel food coloring
Stand up the piping bags or plastic zippered bags in a drinking glass with the tip folded upwards so the batter does not go all the way into the corner of the bag. Spoon the red and blue batters into the 2 bags.
Spray the bundt pan with baking spray that has flour in it.
Cut about ½ inch off the tip of the red batter bag. Pipe the red batter into alternating swirls of the sides of the bundt pan. Just pipe into the edge of the pan, about halfway up from the bottom. Repeat the process with the blue batter.
Spoon about half of the white batter into the bundt pan to fill up the interior of the base. Pipe more of the red batter and blue batter up the sides of the pan if some slid down. Pipe the remaining red and blue batter in alternating dots on top of the white batter. Top it off with the remaining white batter. You do not need to swirl the colors together, as they will naturally settle as they bake.
Bake for 60-70 minutes. Insert a cake thermometer or toothpick into the tallest part of the cake, about 1-2 inches deep. Bake for an additional 5 minutes at a time until the batter no longer comes out wet, or until the cake thermometer turns red.
Let cool in the pan on a cooling rack for 15 minutes. If it has domed, use a serrated knife to trim off the excess so that the cake has a flat surface to sit upon when it comes out of the pan. Then, put a cake board or dish upside down on top of the pan. Use oven mitts to flip the cake over onto the board or dish. Gently shake the pan to release. Let cool completely, about 2 hours, before icing.