Preheat the oven to 350 (F). Coat three 9-inch round cake pans with a nonstick cooking spray.
Mash 16 ounces of thawed frozen strawberries through a strainer over a measuring cup until you get about 1 cup of juice. Reserve the mashed strawberries. Add the 1 cup of juice to a saucepan. Bring to a boil and cook until reduced to 1/4 cup.
Using a food processor, pulse the reserved mashed strawberries until they are finely chopped. Add the 1/4-cup reduced strawberry juice and 1 1/2 teaspoons fresh lemon juice to the chopped strawberries and pulse until blended. Set aside.
In a medium bowl, whisk together 4 cups cake flour, 1 3/4 teaspoons baking powder, and 3/4 teaspoon regular salt. Set aside. In the bowl of a stand mixer fitted with a paddle attachment, beat 2 cups of butter until light and fluffy, then reduce the speed and add 3 cups granulated sugar, beating until smooth. Add 6 eggs and 2 egg yolks, one at a time, beating until blended. Add 3/4 cup of the strawberry puree (from the third step), 1 1/2 teaspoons strawberry liqueur, and 1/4 teaspoon red food coloring and beat until just incorporated.
Keeping the mixer speed on low, alternately add the flour mixture (from the fourth step), 1 cup at a time, alternating with 1/4 cup milk, 2 tablespoons at a time. Beat until smooth.
Divide the batter equally among the prepared pans and bake until a wooden pick inserted into the middle comes out clean, around 30 to 35 minutes. Let the cakes cool in the pans for 10 minutes before turning them out onto a wire rack to cool completely.