In continuation of the series of perovskite oxides that includes 3d(4) cubic BaFeO3 and 4d(4) cubic BaRuO3, 5d(4) cubic BaOsO3 was synthesized by a solid-state reaction at a pressure of 17 GPa, and its crystal structure was investigated by synchrotron powder X-ray diffraction measurements. In addition, its magnetic susceptibility, electrical resistivity, and specific heat were measured over temperatures ranging from 2 to 400 K. The results establish a series of d(4) cubic perovskite oxides, which can help in the mapping of the itinerant ferromagnetism that is free from any complication from local lattice distortions for transitions from the 3d orbital to the 5d orbital. Such a perovskite series has never been synthesized at any d configuration to date. Although cubic BaOsO3 did not exhibit long-range ferromagnetic order unlike cubic BaFeO3 and BaRuO3, enhanced feature of paramagnetism was detected with weak temperature dependence. Orthorhombic CaOsO3 and SrOsO3 show similar magnetic behaviors. CaOsO3 is not as conducting as SrOsO3 and BaOsO3, presumably due to impact of tilting of octahedra on the width of the t2g band. These results elucidate the evolution of the magnetism of perovskite oxides not only in the 5d system but also in group 8 of the periodic table.