Heat oven to 350°F. Grease three 8-inch-round cake pans. Line pans with waxed paper; grease paper.
In bowl, mix flour, cocoa powder, baking powder and salt. In large bowl, beat butter and sugar until creamy. Beat in sour cream, then eggs. On low, beat in flour mixture in 2 batches, alternating with milk. Divide among prepared pans.
Bake in 350°F oven 30 minutes, until springy to touch. Cool in pans 5 minutes. Invert onto racks; remove paper.
In bowl, beat butter, sour cream. Beat in sugar, 3 tablespoons liqueur, vanilla. Filling: Remove 3/4 cup; chill 5 minutes. Frosting: Beat cocoa, remaining liqueur into remaining butter mixture. Fill, stack, frost layers.