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We estimate the upper bound for the $\ell^{\infty}$-norm of the volume formon $\mathbb{H}^2\times\mathbb{H}^2\times\mathbb{H}^2$ 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 Riemennianmanifolds 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 ofclosed Riemannian manifolds covered by $\big(\mathbb{H}^2\big)^n$.

Lower Bound for the Simplicial Volume of Closed Manifolds Covered by $\mathbb{H}^{2}\times\mathbb{H}^{2}\times\mathbb{H}^{2}$