  The $k$-higher Mahler measure of a nonzero polynomial $P$ is the integral of
$\log^k|P|$ on the unit circle. In this note, we consider Lehmer's question
(which is a long-standing open problem for $k=1$) for $k>1$ and find some
interesting formulae for 2- and 3-higher Mahler measure of cyclotomic
polynomials.
