Preheat the oven to 350F, and spray three 6-inch cake pans with baking spray.
In a medium bowl, make the chocolate cake batter. Whisk together the butter and sugar until creamy and slightly fluffy, then add in the egg and egg white. Mix well.
Whisk in the milk, vanilla extract and cocoa, then mix in the flour, baking powder, baking soda, and salt.
Remove about ⅓ of the batter and transfer it to a separate bowl. Set aside.
In another medium bowl, make the vanilla cake batter. Mix together the egg and sugar until well-combined. Add in the softened butter, whisking until creamy and lump-free.
Mix in the flour, baking powder, and salt, then finally stir in the vanilla and milk.
Remove about ⅓ of the vanilla batter, and add it to the separated chocolate batter. Mix these together, as this will be the "center" layer of the ombre cake.
Pour each batter in a separate cake pan, and bake for 20 minutes at 350F, then cover with foil and bake for 8-10 minutes longer, until a toothpick inserted in the center comes out clean.
Once cakes are ready, let cool completely before frosting.
To make the frosting, first you must reduce the pomegranate juice. Pour the juice in a small pot, and set it over medium heat. Bring to a low boil, and let this cook, stirring occasionally, until the liquid reduces to about ¼ cup of thickened syrup. Let cool completely before using.
To make the frosting, beat the butter in a stand mixer fitted with the whisk attachment until smooth and creamy. Slowly add in the cooled pomegranate syrup until completely incorporated.
Add in the powdered sugar, and beat until the frosting comes together. You can add a little bit of pink food coloring for a more intense color.
Frost cake as desired, and top with your favorite sprinkles. Enjoy!