The pilot stated that the purpose of the flight in the multiengine airplane was to build proficiency and to take an acquaintance, who was not a pilot, on a familiarization flight. The pilot described that before departing the airplane had 22 gallons of fuel in the main fuel tanks, and 15 gallons of fuel in the auxiliary fuel tanks, and that the entire flight was conducted utilizing the main fuel tanks. The pilot flew over a practice area for 20 minutes and then returned to the departure airport where he performed two uneventful touch-and-go landings. The pilot added that he miscalculated the fuel consumption rate and thought about 15 minutes of fuel remained for the third landing, which would have been full-stop. He further stated that while turning from the downwind to the base leg of the airport traffic pattern for the third landing, both engines lost total power. The pilot turned toward the runway and attempted to restart one of the engines; however, the attempt was unsuccessful and the airplane impacted trees about ½-mile short of the runway. The airplane sustained substantial damage to the fuselage, empennage, and both wings. The pilot added that there were no preimpact mechanical malfunctions or failures of the airplane that would have precluded normal operation.