We study the Ramanujan sum \(c_{\textbf{m}}(\textbf{n})\) , where \(\textbf{m}\) and \(\textbf{n}\) are integral ideals in an arbitrary number field \(\mathbb {F}/\mathbb {Q}\) . Previous work studied the asymptotic behavior of the average of Ramanujan sums \(c_{\textbf{m}}(\textbf{n})\) over both ideals \(\textbf{m}\) and \(\textbf{n}\) . We extend this investigation to the third moment of averages of Ramanujan sums over arbitrary number fields and obtain the asymptotic formulas for three cases.
