  We estimate the upper bound for the $\ell^{\infty}$-norm of the volume form
on $\mathbb{H}^2\times\mathbb{H}^2\times\mathbb{H}^2$ seen as a class in
$H_{c}^{6}(\mathrm{PSL}_{2}\mathbb{R}\times\mathrm{PSL}_{2}\mathbb{R}\times\mathrm{PSL}_{2}\mathbb{R};\mathbb{R})$.
This gives the lower bound for the simplicial volume of closed Riemennian
manifolds covered by $\mathbb{H}^{2}\times\mathbb{H}^{2}\times\mathbb{H}^{2}$.
The proof of these facts yields an algorithm to compute the lower bound of
closed Riemannian manifolds covered by $\big(\mathbb{H}^2\big)^n$.
