Beat butter until fluffy, gradually add sugar, beating well. Add eggs, one at a time, beating until blended after each. Add rum. Beat till blended.
Combine flour, cocoa, powder, soda, salt and nutmeg. Add to sugar mixture alternately with hot water, beginning and ending with dry things. Beat at low until blended after each addition; stir in extracts.
Pour into 2 greased and floured 9-inch round cakepans. Bake at 350 for 27 minutes. It will test not quite done. Cool in pans on rack 10 min; Remove from pans and then cool completely on them.
Spread 1 cup frosting between layers; frost top and sides with rest. Cover and chill 8 hours. Store in fridge.
Frosting: Beat cream until foamy. Gradually add powdered sugar, cocoa and extracts, beating until blended. Add rum; beat until thick and smooth.