Babylon.
Babylon
The capitol city of the empire.
It was both. It was essentially the capitol city of the Babylonian empire. It was initially just a small Semitic Akkadian city but grew in influence until it gained independence and became a city-state. Note - although the empire is frequently referred to as Babylon, it is more accurately "Babylonia" - with Babylon as the capitol.
Babylon
Babylon was the capital city of Babylonia (Babylonian empire)
During the reign of Hammurabi, the Babylonia Empire controlled the cities of Babylon, Ur, Uruk, Lagash, Kish, ad several others. Biblical records tell us that Babylon controlled the Levant, including Jerusalem, for a time The territories of modern countries that were within the Babylonian empire at one time or another include Iraq, Syria, Turkey, Egypt, Saudi Arabia, Jordan, Iran, Kuwait, Lebanon, Palestine , Israel and Cyprus.
Babylon
Babylon.
Aztec Empire
Babylon!
Babylon
Rome is capitol of Italy, as for the Roman Empire the capitol city was... Rome.