  In a previous paper [arXiv:1901.01681], we presented an analytic construction
of multi-brane solutions in cubic open string field theory (CSFT) for any
integer brane number. Our $(N+1)$-brane solution is given in the pure-gauge
form $\Psi=U Q_\textrm{B}U^{-1}$ in terms of a unitary string field $U$ which
is specified by $[N/2]$ independent real parameters $\alpha_k$. We saw that,
for various sample values of $N$ $(=2, 3, 4, 5,\cdots)$, $\alpha_k$ can be
consistently determined by two requirements: The energy density from the action
should reproduce that of $(N+1)$-branes, and the EOM of the solution against
the solution itself should hold. In this paper, we complete our construction by
determining $\alpha_k$ satisfying the two requirements for a generic $N$. We
find that each $\alpha_k$ is given in a closed form by using the Bernoulli
numbers. We also present some supplementary results on our solution; the energy
density of the solutions determined from its gravitational coupling, and the
unitary string field $U$ as an exponential function.
