Is Peru a state?

The word "state" has two different meanings. The term "sovereign state" means a country or nation that is not part of another country. In the US, the word "state" means one of the 50 separate political entities that form the entire country as a federal (federated) republic.

Peru is a separate country, in western South America. It can be described as a "nation-state", but it is not a state in some larger government.