Integrals involving four Macdonald functions and their relation to 7zeta(3)/2

A family of multiple integrals over four variables is rewritten in terms of a family of simple integrals involving the product of four modified Bessel (Macdonald functions). The latter are shown to be related to 7zeta(3)/2. A generalization to 2n integration variables is given which yields only zeta at odd arguments.