Single-phase samples of cubicREBa2Fe3O8+wwithRE=Gd, Eu, Sm, Nd were synthesized and equilibrated at 900°C in atmospheres with controlled partial pressures of oxygen. The oxygen content parameterwranged from approximately -0.30, which is the lower decomposition limit, to betweenw=0.17 forRE=Gd andw=0.37 forRE=Nd, achieved in O2without crossing the upper limit. According to57Fe Mössbauer spectroscopy, all samples are antiferromagnets at room temperature, with iron in high-spin states (S=2 for Fe2+and Fe4+;S=5/2 for Fe3+). The contents of divalent or, alter- natively, tetravalent iron states are consistent with the stoichiometry of the samples. At the stoichiometric composition (w=0), all Mössbauer components correspond to trivalent iron, differing only in the coordination geometries of their oxygen neighborhoods. The sum-up of the observed coordination numbers shows that the oxygen disorder in these cubic (by X-ray diffraction) phases is a linear combination of the two limiting cases of oxygen vacancy distribution: binomial (random) and ordered (one vacancy per every third pseudocubic cell). This corresponds to a gradual change from the long-range order seen in triple-perovskite-type phases (RE=Er to Dy) via a short-range order seen in the present systems (RE=Gd to Nd) to a fully random disorder (RE=La). Eventual variations inwaffect the coordination statistics in details, but change the overall picture very little.