Preheat the oven to 350 degrees F.

Butter one 4 by 3-inch cake pan, one 6 by 3-inch cake pan and one 8 by 3-inch cake pan. Line the bottoms with parchment paper, and butter and flour the pans.

Sift the flour, cocoa, baking soda, and salt together in a medium bowl.

In the bowl of an electric mixer fitted with a paddle attachment, cream the butter and sugars on high speed until light, approximately 5 minutes. Add the eggs and vanilla and mix well. Combine the buttermilk, sour cream, and coffee. On low speed, add the flour mixture and the buttermilk mixture alternately in thirds, beginning with the buttermilk mixture and ending with the flour mixture. Mix the batter only until blended.

Divide the batter between the three pans and smooth the tops with a spatula. Bake on the middle rack of the oven as follows: for the 4-inch pan 45 to 50 minutes, or until a toothpick comes out clean; for the 6-inch pan 70 to 75 minutes, or until a toothpick comes out clean; and for the 8-inch pan 85 to 90 minutes, or until a toothpick comes out clean . Cool the cakes in the pans for 10 minutes each on a cooling rack, carefully remove from the pans and allow to finish cooling.

Place the 8-inch cake on a serving plate, flat side up. Frost the top and sides of that layer with buttercream. Place the 6-inch cake in the center of the top of the 8- inch cake, flat side up, and frost the top and sides. Place the 4-inch cake in the center of the top of the 6-inch cake, flat side down. Frost the top and sides of that layer with buttercream. Spread any remaining buttercream over the cake evenly.

Chop the chocolates and place them in a heat-proof bowl set over a pan simmering water. Stir until melted and set aside until cooled to room temperature.

Mix the egg whites, sugar, cream of tartar, and salt in the bowl of an electric mixer fitted with a whisk attachment. Place the bowl of egg whites over the pan of simmering water and heat the egg whites until they are warm to the touch, about 5 minutes. Return the bowl to the electric mixer and whisk on high speed for 5 minutes, or until the meringue is cool and holds a stiff peak.

Add the butter, 1 tablespoon at a time, while beating on medium speed. Scrape down the bowl, add the melted chocolate, vanilla, espresso, and rum, if using, and mix for 1 minute or until the chocolate is completely blended in. If the buttercream seems very soft, allow it to cool, and beat it again.