  We present an analytic construction of multi-brane solutions with any integer
brane number in cubic open string field theory (CSFT) on the basis of the $KBc$
algebra. Our solution is given in the pure-gauge form
$\Psi=UQ_\textrm{B}U^{-1}$ by a unitary string field $U$, which we choose to
satisfy two requirements. First, the energy density of the solution should
reproduce that of the $(N+1)$-branes. Second, the EOM of the solution should
hold against the solution itself. In spite of the pure-gauge form of $\Psi$,
these two conditions are non-trivial ones due to the singularity at $K=0$. For
the $(N+1)$-brane solution, our $U$ is specified by $[N/2]$ independent real
parameters $\alpha_k$. For the 2-brane ($N=1$), the solution is unique and
reproduces the known one. We find that $\alpha_k$ satisfying the two conditions
indeed exist as far as we have tested for various integer values of $N$ $(=2,
3, 4, 5, \cdots)$. Our multi-brane solutions consisting only of the elements of
the $KBc$ algebra have the problem that the EOM is not satisfied against the
Fock states and therefore are not complete ones. However, our construction
should be an important step toward understanding the topological nature of CSFT
which has similarities to the Chern-Simons theory in three dimensions.
