A theoretical study of Heisenberg exchange and double exchange interactions in iron-sulphur superclusters is presented. The clusters can play an important role in biological systems (proteins and enzymes) acting as so-called active centers. The cluster with valence 4+ can be modeled by four Fe(III) and two Fe(II) ions. An idealized structure of double cubane has been considered instead of a more realistic defected double cubane structure of lower symmetry. Possible spin ground states (S=0,1,2,3,4,5,6) have been predicted. The total spin S=6 is preferred within a partially ferromagnetic region if a Heisenberg exchange parameter [between the nearest Fe(III) ions] J(2)< 0 although increase of a double exchange parameter b leads to narrowing of those region in favor of the states with lower spins. If J(2)> 0, domination of the spin states with S=0 and S=4 is expected for larger values of the parameter b. The state of S=4 is predicted for J(2)> 0 in agreement with experimental data.