I think of the U.S. bases around the world more as quasi-police stations than colonies or parts of an empire. When a nation has an empire, there's usually money flowing IN from the colonies. In our case, the money goes in the other direction.

For anyone who is interested in a comparing and contrasting a super power of the ancient world with one from today, there is a wonderful book which I highly recommend: "Empires of Trust --- How Rome Built and America is Building a New World"