I was under the impression that Olympic sports venues rarely if ever earn back the investment - just like big city sports arenas tend not to, if you consider all the costs and tax breaks local governments have to give the investors and sports teams. It's all about prestige, providing sports fans what they want, providing construction firms with the money and contracts they want, and diverting attention away from problems in governance. Despite the poor return on investment, countries and cities continue to vie to become major sports venues.
Russia greatly strengthened it's already strong prestige at Sochi in figure skating. They also brought a lot of high level coaches back to Russia. So the effort and economic support paid off, in that area and sense. Very expensive, but still.
I don't know all that much about Russian politics, but perhaps the Sochi Olympics have partly been a good excuse to bring Russian military forces around Crimea, prior to it's invasion, and to the Caucuses, where Russia has frequent opposition. If so, perhaps it was worth it, from Putin's perspective. In other words, perhaps the real game, to him, was geopolitical and military dominance.