The Book of Nathan, also known as the Records of Nathan, was a work known to the writers of the Old Testament books of First and Second Chronicles. The record there corroborated the information the authors were writing about David and Solomon.
While it is referenced in the Bible, it is not a canonical book of the Bible. The book's title is eponymous, being the writing of the prophet Nathan. If Nathan was an author of First and Second Samuel, it is possible that textual references to this book may actually be referring to the Books of Samuel. It is also possible that the writers are adhering to the law concerning two or three witnesses.