2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164492Let $(X,\mathcal{B},μ, T)$ be a measure preserving system. We prove the pointwise convergence of averages along cubes of $2^{k}-1$ bounded and measurable functions for all $k$.12 pages, latex, initially. Now it 10 pages long. It is modified accordingly to the changes made in the paper math.DS/0305388 which deals with the averages of three and seven functions and the weakly mixing caseDynamical Systems37A30text