  The SU(3) lattice gauge theory is reformulated in terms of SU(3) prepotential
harmonic oscillators. This reformulation has enlarged $SU(3)\otimes U(1)
\otimes U(1)$ gauge invariance under which the prepotential operators transform
like matter fields. The Hilbert space of SU(3) lattice gauge theory is shown to
be equivalent to the Hilbert space of the prepotential formulation satisfying
certain color invariant Sp(2,R) constraints. The SU(3) irreducible prepotential
operators which solve these Sp(2,R) constraints are used to construct SU(3)
gauge invariant Hilbert spaces at every lattice site in terms of SU(3) gauge
invariant vertex operators. The electric fields and the link operators are
reconstructed in terms of these SU(3) irreducible prepotential operators. We
show that all the SU(3) Mandelstam constraints become local and take very
simple form within this approach. We also discuss the construction of all
possible linearly independent SU(3) loop states which solve the Mandelstam
constraints. The techniques can be easily generalized to SU(N).
