Back in November, Azadliq Radiosu published an article on the costs of the European games. It referenced an article in a publication called Business New Europe. There, speaking on the costs of the games, the article noted an $8billion estimate in total costs of the upcoming games. This estimate was based on October 2013 projections for state budget actually noted by the authorities themselves.
Since then, the article is not accessible. However, the issue is still available if you visit the Business New Europe website.
By the way, the "sponsors" of this issue are TEAS (lobby organization with headquarters in London and run by the son of the Ministry of Emergency Situation). Pasha Bank, has links to the ruling government.
What is interesting that the government of Azerbaijan still denies the costs. It says the total costs of the games is EUR960mn [AZ] and that all final costs would be announced once the games are over. The opening alone of the games cost $95million.
The government of Azerbaijan in the meantime is trying to lower the importance of the costs while emphasizing the image boosting side of the games. But to me looks like Azerbaijani government just spent billions to highlight the crackdown, the human rights issues and everything that is not working in the country.