The gemara in Megila 6b refers to איטליא של יון זה כרך גדול של רומי, which translates literally as: Italy of Greece, this is the great city of Rome.
This seems odd insofar as I know, Italy never belonged to Greece.
Also problematic is referring to Italy as being part of Rome, the opposite is true.
Soncino however translates this as
‘Greek Italy’ is the great city of Rome
and brings an explanation in this note:
(15) [home is so designated on account of the great influence of the Greek civilization on the Roman, v. Bacher, REJ, XXXIII, p. 190.]
While this addresses my first issue, it does not address my second issue. I also don't especially like this idea. I am looking for a different explanation of this line.
Please take into account that this phrase is stated by Ulla who lived into the fourth century, and would probably have a decent idea about Rome and it's history.