In this talk I will discuss some recent results in the pointwiseconvergence of some averages for commuting transformations. Recently we have shown the existence of the limit of cubic averages arising from systems with commuting transformations. I will show the main ideas in the proof, which combine the notions of sated extensions by T. Austin, magic extensions by B. Host and ideas by W. Huang, S. Shaoan X. Ye on introducing a topological structure to build a strictly ergodic model for an ergodic system.