The topological properties of cubic structures which have been proposed as models for the cholesteric blue phases (BP) are considered. When the space of the order parameter is restricted to the standard one for biaxial nematics [SO(3)/$D_2$] then, as a consequence of the cubic symmetry, these structures must have disclinations. The usual classification scheme, wherein defect lines are characterized by the conjugacy classes of the fundamental group appropriate to a biaxial system, is used; some exceptions are also noted. For each of the three groups studied [body-centered-cubic $O^5$ (I432) and $O^8$ (I$4_1$32), and simple-cubic $O^2$ (P$4_2$32)] two aspects are considered: general symmetry constraints on disclinations and the topological properties of equilibrium order-parameter distributions as found from Landau-theory calculations. For $O^5$ and $O^2$, there are two nonequivalent symmetry axes upon which there must be disclinations. When they are characterized by a uniaxial order parameter, one must be uniaxial positive and the other uniaxial negative in order for the topology to be consistent with the space-group symmetries. This is not the case for $O^8$ where only one type of defect line, located on the threefold axes, is topologically required. The order-parameter fields obtained from Landau–free-energy minimization have, except in the case of $O^5$, additional disclinations. In particular, the three structures described by the $O^8$ space group are found to have distinctly different networks of defect lines. These, as well as the additional disclination found in the $O^2$ structure, are examined and their group structures were determined. Finally, some open questions and directions for future work are examined.