In the 1993 Western Number Theory Conference, Richard Guy proposed Problem 93:31, which asks for integers n representable by
${(x+y+z)^3}/{xyz}$
, where
$x,\,y,\,z$
are integers, preferably with positive integer solutions. We show that the representation
$n={(x+y+z)^3}/{xyz}$
is impossible in positive integers
$x,\,y,\,z$
if
$n=4^{k}(a^2+b^2)$
, where
$k,\,a,\,b\in \mathbb {Z}^{+}$
are such that
$k\geq 3$
and
$2\nmid a+b$
.