The electronic correlations on a C$_{20}$ molecule, as described by an
extended Hubbard Hamiltonian with a nearest neighbor Coulomb interaction of
strength $V$, are studied using quantum Monte Carlo and exact diagonalization
methods. For electron doped C$_{20}$, it is known that pair-binding arising
from a purely electronic mechanism is absent within the standard Hubbard model
(V=0). Here we show that this is also the case for hole doping for $0