"We live in the Federal Republic of Germany."
Translation:Wir wohnen in der Bundesrepublik Deutschland.
Yes; it's wrong because of the -s on Deutschland.
It's the Federal Republic that is called Germany, not the Federal Republic that is in Germany (like the United States of America).
Similarly, the "City of Hamburg" would be "Stadt Hamburg" and not "Stadt Hamburgs" -- no genitive for this kind of construction.