Third-order bounds on the conductivity of a random stacking of cubes a
re constructed. Since a random stacking of cubes is a symmetric cell m
aterial the bounds are determined by a Miller parameter G [J. Math. Ph
ys. 10, 1988 (1969)] that is independent of volume fractions. This par
ameter is evaluated with a boundary integral technique to G=0.13751642
93203.