When writing an essay, if I have cited some paragraph from a book in the footnotes, do I need to include that book in the bibliography after the essay? Or I only need to include books that have not been cited in the bibliography?
If you are using OSCOLA style, then the footnotes will include all the necessary bibliographic information and a bibliography/works cited is not required. See, for example, the Oxford University Undergraduate Law Journal, which follows OSCOLA style.
Generally speaking, most styles that require a Works Cited/Bibliography have "in-line" or "parenthetical" citations, rather than footnotes (e.g., APA style). The key thing to remember is that the purpose of citations is to allow your readers to consult your sources for themselves and, where you are citing secondary sources, to give credit to the authors for their contribution to the scholarly conversation.