  We study the electronic states of giant single-shell and the recently
discovered nested multi-shell carbon fullerenes within the tight-binding
approximation. We use two different approaches, one based on iterations and the
other on symmetry, to obtain the $\pi$-state energy spectra of large fullerene
cages: $C_{240}$, $C_{540}$, $C_{960}$, $C_{1500}$, $C_{2160}$ and $C_{2940}$.
Our iteration technique reduces the dimensionality of the problem by more than
one order of magnitude (factors of $\sim 12$ and $20$), while the
symmetry-based approach reduces it by a factor of $10$. We also find formulae
for the highest occupied and lowest unoccupied molecular orbital (HOMO and
LUMO) energies of $C_{60{\cdot}n^{2}}$ fullerenes as a function of $n$,
demonstrating a tendency towards metallic regime for increasing $n$. For
multi-shell fullerenes, we analytically obtain the eigenvalues of the
intershell interaction.
