Can a federal state be a nation-state?
Yes, a federal state can be a nation state at the same time. One term is primarily focussed on the governmental structure, while the other puts more emphasis on the cultural unity and commonalities of the population within the country being described.
"Federal" refers to a form of government in which some powers are designated to a central governmental authority, while other governmental powers and responsibilities are designated to other, usually more locally-based authorities. In the United States, the federal government is responsible for defense and conducting foreign policy on behalf of the nation, for example, while individual states are in charge of education within each particular state.
The term "nation-state" describes a political system that serves the citizens of a geographic and cultural area as the legitimate government for that area.