In a large bowl beat the egg yolks until thick. Gradually add the granulated sugar, beating until light. Add the cream,beating until very well combined. Slowly stir in the Cognac and the rum. Refrigerate the mixture, covered, until well chilled. About 1 hour before serving, beat the egg whites until foamy. Gradually add the confectioners' sugar, beating well after each addition, and continue beating until soft peaks form. Gently fold the egg whites into the egg yolk mixture. Refrigerate the eggnog, covered, until serving time.