That's a claim made by Herodotus, though in his telling he really only claims he ran to sparta from Athens in two days and made his way back at some point. He was also famous even in his own day to make up stories and greatly exaggerate for dramatic effect, and his story is from 40 years after the events occurred.

In reality, it really doesn't make sense for one runner to do the whole trek. Ancient greece was famous for having a relay system of runners to deliver important news, similar to the pony express, but without the ponies. It would have been a lot faster and more secure to use the relay system instead of having a random unheard of dude do the whole run.