CAKE: Preheat oven to 325 F. Generously butter and flour a 10-inch springform pan. Cream together the butter and sugar. Beat in the egg yolks, one at a time, and then add the next 4 ingredients, beating until smooth. Mix in the vanilla and rum. Sift together the cinnamon, flour and baking powder and add to the batter, mixing well. Beat the egg whites until stiff--BUT NOT DRY--and fold them into the batter. Pour the batter into the pan and bake for 1 1/2 hours or till a knife inserted in the center comes out clean. Allow the cake to cool for about 15 minutes in the pan, then slide a knife between the sides of the cake and the detachable side of the springform pan. Remove the pan. While the cake is cooling, prepare the frosting. Cream together the butter and powdered sugar. Add the rest of the ingredients and beat till smooth. When the cake is cool, carefully slice it in half horozontally and spread the jam or cooked apricots between the layers. Reassemble the cake and spread the frosting on the top and sides. If you wish--decorate with almonds.