DURING IFR FLIGHT IN VFR CONDITIONS THE PILOT REPORTED LOW FUEL SITUATION TO APPROACH CONTROL. THE AIRCRAFT WAS IN THE VICINITY OF SEVERAL LIGHTED AIRPORTS AT THAT TIME. THE AIRCRAFT LOST POWER AND MADE FORCED LANDING AT NIGHT IN MOUNTAINOUS TERRAIN WHERE AN INFLIGHT COLLISION WITH TERRAIN OCCURRED. THE PILOT HAD FILED AN IFR FLIGHT PLAN FROM MIAMI TO KNOXVILLE. THE AIRCRAFT ARRIVED IN THE KNOXVILLE AREA EARLIER THAN PLANNED AND THE PILOT DECIDED THAT SUFFICIENT FUEL REMAINED TO COMPLETE THE FLIGHT TO LOUISVILLE. THE FUEL GAUGES INDICATED TWO HOURS RANGE FOR THE ONE HOUR FLIGHT. DURING PREFLIGHT INSPECTION AT MAIMI THE PILOT REPORTED THAT THE RIGHT FUEL TANK WAS FILLED TO FILLER CAP; THE LEFT FUEL TANK WAS FILLED TO A LEVEL THAT COULD BE FLET WITH FINGER TIPS. THERE WAS NO REPORT OF ANY MALFUNCTION OR FAILURE OF THE AIRCRAFT PRIOR TO THE ACCIDENT.