and it will cost $318,181,000,000 to use the current shuttle to put it in orbit(based on $250m per launch, a conservative price). Over 1200 launches. If we assume a new shuttle with a $40million(man is that optimistic) per launch cost, and a 30,000lb payload, it will take 934 launches, at a total cost of $37,333,000,000. As you said, it will take half a century to do. Let's say we spend 5 billion developing, building, and launching a probe to go to a NEO and knock it into orbit to serve as your counter wieght. BTW, this asteriod would probably tip the scales against your cube by several million tons.