Lots of people rank the world’s universities in lots of different ways.  One of the more reliable rankings is from the Times Higher Education Supplement: they write about the subject all the time, and their views are respected world wide.  Their 2022 rankings have Cambridge in 5th position worldwide, and 2nd in the UK.

This is good, but their historic rivals Oxford are doing better: first overall.  Cambridge would love to reverse those rankings. The slots between the Oxbridge rivals are filled by Americans: California Institute of Technology, Harvard, and Stanford.