Four novel cobalt-substituted polyoxometalates having cobalt cores exhibiting cubane or dicubane topologies have been synthesized and characterized by IR, elemental analysis, electrochemistry, UV-vis spectroscopy, X-ray single-crystal analysis, and magnetic studies. The tetracobalt(II)-substituted polyoxometalate [Co-4(OH)(3)(H2O)(6)(PW9O34)](4-) (1) consists of a trilacunary [B-alpha-PW9O34](9-) unit which accommodates a cubane-like {(Co4O4)-O-II} core. In the heptacobalt(II,III)-containing polyoxometalates [Co-7(OH)(6)(H2O)(6)(PW9O34)(2)](9-) (2), [Co-7(OH)(6)(H2O)(4)(PW9O34)(2)](n)(9n-) (3), and [Co-7(OH)(6)(H2O)(6)(P2W15O56)(2)](15-) (4), dicubane-like {(Co6CoO8)-Co-II-O-III} cores are encapsulated between two heptadentate [B-alpha-PW9O34](9-) (in 2 and 3) or [alpha-P2W15O56](15-) (in 4) ligands. While 1, 2, and 4 are discrete polyoxometalates, 3 exhibits a polymeric, chain-like structure that results from the condensation of polyoxoanions of type 2. The magnetic properties of these complexes have been fitted according to an anisotropic exchange model in the low-temperature regime and discussed on the basis of ferromagnetic interactions between Co2+ ions with angles Co-L-Co (L = O, OH) close to orthogonality and weakly antiferromagnetic interactions between Co2+ ions connected through central diamagnetic Co3+ ion. Moreover, we will show the interest of the unique spin structures provided by these cubane and dicubane cobalt topologies in molecular spintronics (molecular spins addressed though an electric field) and quantum computing (spin qu-gates).