To win a cultural victory keep your empire small (no more than 4 cities), liberate city states, burn the rest. I'm currently trying to get a fast cultural victory with the Arabs for the Gauntlet, and on my first attempt I found it easy but boring. I could only build 3 cities (desert after that and city states blocking) with only one luxury resource, however nobody was a threat. Don't bother about their wars (other than accepting the secrecy pacts), keep your borders close, and build NO TROOPS. Even gave my initial warrior to a city state halfway too. Having no troops for about 3500 years is scary . However got out 5 mechanised infantry, when started the Utopia wonder, and with then cleared the continent by the time it finished. (Rushing it through with successive golden ages too).