Preheat the oven to 350 (F). Butter three 9-inch round cake pans, line the bottoms with parchment paper, and spray with nonstick cooking spray.
In a medium bowl, whisk together 4 cups cake flour, 3/4 teaspoon salt, 1/2 teaspoon baking powder, and 1/4 teaspoon baking soda.
In the bowl of a stand mixer fitted with a paddle attachment, beat 1 1/2 cups unsalted butter and 3 cups granulated sugar on medium speed until light and fluffy, scraping the bowl as necessary, about 3 minutes. Add 8 eggs, one at a time, beating until just combined and scraping the bowl as necessary. Add 1 1/2 teaspoons vanilla extract and 1/4 teaspoon rum extract and beat until just combined.
Reduce the mixer speed to its lowest setting and alternately add the flour mixture (from the second step) and 1 cup sour cream to the batter mixture, beginning and ending with the flour mixture until just combined but smooth.
Set aside and make the chocolate batter.