Isn't some of that US$51bn for other amenities like new hotels etc... And of course after the games there are plans to have a F1 race at Sochi, the first scheduled to take place on the 12th October (the 16th round)
Beijing had a population close to 10 million and it couldn't even absorb all that infrastructure built for the Olympics. Sochi is barely 1/20 the size of Beijing. This is going to be worse than what happened to all that leftover infrastructure in Athens.