Although liquid water and ice are characterised by predominantly tetrahedral coordination, small water clusters often exhibit a cubic structural motif. In this article, the stability of hydrogen-bonded water nanostructures in the form of n 1×n 2×n 3 cuboids is investigated. The requirement for complete hydrogen bonding imposes a strong constraint on their structure. The equations of the donor–acceptor balance are derived, from which all possible forms of completely hydrogen-bonded cuboids are deduced. The flexible non-additive AMOEBA potential is used for geometric optimisation of the set of configurations with different directions of hydrogen (H-) bonds. It has been established that the majority of completely hydrogen-bonded structures are formed by one layer of fused cubes. The lowest energy configurations of the, in fact, bilayer structures are formed by trans-configurations of transverse pairs of molecules, although some H-bonds are broken in this case. It is noted that the structure of the cuboids may result from the assembly of short nanotubes and smaller cuboids. On the other hand, unrealised H-bonds at the corners of the cuboids make it possible to assemble larger bilayer structures.