As simple as that. It can’t be "State of the Federal Republic”, because civitatum is plural (civitatum is genitive plural from civitas civitatis).
Can you check if it is not foedaratarum instead of “federatum”? Feradatum is strange here, it would be an adjective in neuter, meaning “federated, united”, but it doesn’t agree with any other noun in the sentence. If you had “foederatarum”, as in my diploma (see below), it would agree with civitatum, which is more logical, and literally means “of the united states”, or “of the united cities”. And Reipublicae means “of the Country/State/Nation” so, the expression can be rendered “Year 182 of the United States of the Country” (not to repeat “state”), or, more simply, "of the United States".

My dictionary gives this translation for “The United States”: Foederatae Americae Septentrionalis Civitates, i.e., United States of North America (in nominative case).
And this glossary on-line:
http://wredmond.home.texas.net/ulittera.html
translates it as follows: Status Foederati or Uniti Status or Civitates Foederatae Americae (Septentrionalis)

Again, this dictionary gives a similar translation:
http://www.woordenboek.eu/vertaling/Latijn/ Civitates Foederatae Americae


It cannot be Georgetown: This city was founded on 1751, 38 years before the United States. See this link:

http://en.wikipedia.org/wiki/Georgetown,_Washington,_D.C.

I have just translated a diploma of the Georgetown University, and it uses almost the same expression, “Civitatum Reipublicae Foederatarum anno CCXVIII” that is, the year 218 of the United States, and this is confirmed because the year of the issue of the diploma was MMVII, or 2007, precisely 218 years after the existence of the United States in 1789 (although the Constitutional Convention dates from 1787, the first President and the actual organization of the state dates from 1789).
So, the dates of my diploma and yours match exactly, since you say that it was issued in 1971, that is, 182 years after the existence of the United States.