The Mahler measure of $ (x+1/x)(y+1/y)(z+1/z)+\sqrt{k} $

In this paper we study the Mahler measures of reciprocal polynomials \begin{document}$ (x+1/x)(y+1/y)(z+1/z)+\sqrt{k} $\end{document} for \begin{document}$ k = 16 $\end{document} , \begin{document}$ k = -104\pm60\sqrt{3} $\end{document} , \begin{document}$ 4096 $\end{document} and \begin{document}$ k = -2024\pm765\sqrt{7} $\end{document} . We prove six conjectural identities proposed by Samart in [ 16 ].