January 1871 in Versailles. But that was the "2nd Reich", a mornarchy which is not exactly modern day Germany as stated in your question. It also had totally different borders. Looking at the formulation of your question I would consider Arvens answer quite correct. Of course you do have a point in saying that the rather loose federation of states became the nation Germany back then, but still the formulation modern day Germany doesn't really fit with all the changes that happened afterwards.