Cambridge University is certainly a wonderful university, and studying at a university in a different country from the country in which one grew up has additional educational advantages. But would a United States student be able to afford to study at Cambridge, if the main issue in shopping for local universities is cost?

Cambridge (where I did two degrees) has plenty of funding for non-UK and non-EU students.

It's less and harder to come by for undergrads, but postgrads of all nationalities have a very strong chance of being fully funded.

Don't get me wrong, it's still tough, but no tougher than what I understand the life of a postgrad in the US is :)