In a large bowl, using an electric mixer, beat cream, cream cheese, and confectioners sugar until combined. In a small bowl, combine coffee and rum.
In a 2-quart baking dish, lay half the cake slices in a single layer, trimming to fit. Brush with half the coffee mixture. Top with half the cream mixture and half the chocolate. Repeat. Dust top with cocoa powder. Cover and refrigerate at least 4 hours before serving.
Make it ahead and store, covered, up to 1 week.