The cubic perovskite BaRuO(3) has been synthesized under 18 GPa at 1,000 degrees C. Rietveld refinement indicates that the new compound has a stretched Ru-O bond. The cubic perovskite BaRuO(3) remains metallic to 4 K and exhibits a ferromagnetic transition at T(c) = 60 K, which is significantly lower than the T(c) approximately = 160 K for SrRuO(3). The availability of cubic perovskite BaRuO(3) not only makes it possible to map out the evolution of magnetism in the whole series of ARuO(3) (A = Ca, Sr, Ba) as a function of the ionic size of the A-site r(A,) but also completes the polytypes of BaRuO(3). Extension of the plot of T(c) versus r(A) in perovskites ARuO(3) (A = Ca, Sr, Ba) shows that T(c) does not increase as the cubic structure is approached, but has a maximum for orthorhombic SrRuO(3). Suppressing T(c) by Ca and Ba doping in SrRuO(3) is distinguished by sharply different magnetic susceptibilities chi(T) of the paramagnetic phase. This distinction has been interpreted in the context of a Griffiths' phase on the (Ca Sr)RuO(3) side and bandwidth broadening on the (Sr,Ba)RuO(3) side.