FOR CAKE:
1. Preheat your oven to 350°F / 177°C. Grease 3 (8-inch) cake pans, and line the bottoms with parchment paper rounds. Set aside.

2. In a medium bowl, add in flour, baking powder, baking soda, and salt. Whisk to combine, and set aside.

3. In a large bowl, combine butter, oil, and sugar. Using an electric mixer fitted with the paddle attachment, or a whisk by hand, cream together until pale in color and fluffy (about 2 minutes with an electric mixer set to medium speed or 3 minutes by hand).

4. Add the eggs and egg whites to the butter mixture, one at a time, beating well after each addition until incorporated. Add butter vanilla flavoring and sour cream, and whisk to combine.

5. Alternate mixing dry ingredients and milk into the butter mixture. Start by whisking in about half of your dry ingredients, followed by all of the milk. Mix in the remaining dry ingredients until just combined. Take care not to over mix.

6. Pour 1/3 of the plain cake batter into one of your prepared cake pans, and spread to even. Set aside. 

7. Divide the remaining batter into 2 separate bowls. Color one bowl of batter with 3 drops of blue liquid gel food coloring and color the other bowl with 8 drops. Pour the batters into the other 2 prepared cake pans, and spread to even.

8. Bake the cakes in the center of your preheated 350°F / 177°C oven for 20 to 25 minutes, or until a skewer inserted into the center of the cake comes out clean.

9. Cool the cakes for about 10 minutes in the pans. Turn the cakes onto a wire rack, remove the parchment bottoms, and set aside to cool completely to room temperature.

FOR BUTTERCREAM FROSTING:
1. Place your butter in a large mixing bowl. Using an electric mixer fitted with the paddle attachment, cream the butter on high speed for 2 to 3 minutes, or until it fluffs up and lightens in color. 

2. Add powdered sugar and salt to the butter and mix on low speed to combine. Once the sugar is dissolved, cream on high speed for another 2 minutes.

3. Add butter vanilla flavoring and 3 tablespoons of milk. Beat on high speed for 1 minute, or until everything is well combined and the mixture is light and fluffy. If needed, gradually mix in more milk until the frosting reaches a spreadable consistency.

ASSEMBLY:
1. Level and trim off any browned areas on the cakes. Lay the darkest colored layer onto your cake stand and spread about 1/2 a cup of the darkest colored frosting on top. Lay the lighter blue cake layer on top and spread over about 1/2 a cup of the lighter blue colored frosting. Top with the plain cake layer.

2. Spread the white frosting on the top and upper third of the cake. Spread the lighter blue frosting around the center of the cake, and the darkest blue frosting around the bottom third of the cake.

3. Use an offset spatula to smoothen the frosting on the top and sides of the cake. Decorate with sprinkles, edible pearls, and white chocolate snowflakes.