Abstract In the quasi-free electron model, which is widely used in modern solid-state physics, the Fermi surface spreads into a sphere in the Brillouin zone, i.e., the Fermi Sphere. The Fermi Sphere exists widely in metal systems, no matter whether the crystal is in a body-center cubic, face-center cubic, or hexagonal close-packed lattice. Here, we report a class of compounds stabilized at high pressure with a Rubik's cubic Fermi surface, in which the representative example is P m-3n-CaCl3. Our quantum-mechanical variable- composition evolutionary simulations predicted the thermal stabilities of CaCl3, and the tight-binding model revealed its unique Fermi surface originates from the quasi-one- dimensional interaction, structural symmetric protection, and particle-hole symmetry breaking. Furthermore, by its flat and steep band structure, CaCl3 has a huge span of effective mass from 9.08×103 me (super-heavy) to 5.13×10-4 me on the Fermi level, which supplies an interesting platform for quasiparticle research.