A soft phonon, which contributes to the strong vibrational anharmonicity and plays an important role in determining the phase stability of materials, is a hallmark of cubic perovskites. The coupling among phonons, charges, orbitals and spins in perovskites has been continuously creating exotic phenomena for new applications. However, a comprehensive overview on room-temperature phase stabilities and vibrational anharmonicites of cubic perovskites is very limited. Here, we use multi-tiered high-throughput computational screening to chart out room-temperature stabilities and vibrational anharmonicity landscapes for the full spectrum of 3819 cubic ABX 3 perovskites, encompassing the chemical space of halides, oxides and chalcogenides. We show that halides are systematically more stable and less anharmonic than oxides/chalcogenides. New metrics are developed to quantify the significance of higher order force constants to the strong anharmonicities in room-temperature stable perovskites through both perturbative and temperature-dependent effective potential approaches. The new database and theoretical methods established in this work pave a pathway to deepen the fundamental understanding of lattice dynamics and facilitate the developments of mutifunctional materials with designed physical and chemical properties, such as thermal insulators and high-entropy perovskites.