The ground-state structures of water hexamer and several deuterated variants are studied by using the diffusion Monte Carlo (DMC) method. We demonstrate that a recently developed guided DMC approach allows us to study these systems using substantially smaller ensembles than are required for standard DMC approaches. DMC calculations of the ground states of (H2O)(6) and (D2O)(6) using the MB-pol potential with 50 000 walkers and a 1 au time step show that for (H2O)(6) the cage structure is 51 +/- 7 cm(-1) lower in energy than the prism structure. In the case of (D2O)(6), the two structures have nearly equal energies (Delta E = 9 +/- 11 cm(-1)). The structures of the singly substituted, (H2O)(D2O), and (H2O)(5)(D2O), variants of water hexamer are also explored to identify the impact of the location of the unique water molecule on the relative stability of the possible structure. The effect on the stability of the hydrogen bond on whether a hydrogen bond has an OD or OH bond as the donor is also explored.