Roberto started learning martial arts aged six in his home town of Turin. He began with Judo but would soon progress to kickboxing despite initial attempts by his parents to discourage him. Through his teen years he attended several competitions in full contact kickboxing and boxing winning the Italian title at amateur level. In 1995 he started to learn Thai-boxing under coach Marco Franza and would turn pro not long after. In 2001, after picking up a number of victories on the domestic scene or across the border in France, Roberto had his first shot at a major title. He faced Carlos Heredia for the I.S.K.A. world title, winning a decision victory after twelve rounds – something Cocco was not used to, having usually faced opponents over three to five rounds. As a new world champion, doors opened for Roberto and he found himself in position for more honours; defeating Stephan Mbida to claim the W.P.K.C. intercontinental belt, and then going across to São Paulo, Brazil to unify the I.S.K.A. and U.W.K.F. world titles. Throughout 2003, Cocco would defend his I.S.K.A. belt for the second time and win the W.K.N. world title by defeating Carlos Heredia once again, this time only taking one round as opposed to twelve, in a TKO victory. In 2003 he signed with the recently created SuperLeague, defeating Foad Sadeghi by knockout in his organizational debut in Vienna. By joining the promotion Roberto would face a much stiffer rate of competition, with many of his rivals European and world champions with plenty of fight experience. He found this out to his cost when he faced Joerie Mes in his next SuperLeague match, losing by KO in the fourth round. Between 2003 and 2006, Roberto had a losing record with SuperLeague, good wins against Foad Sadeghi and Moises Baptista De Sousa tempered by a number of defeats, finishing with a 2 and 7 record with the promotion. He had some success on other circuits, however, defeating Roberto Castro in 2005 to claim the W.A.K.O. Pro world title. As SuperLeague folded, Cocco started focusing more on professional boxing defeating former kickboxing rival Alexander Dredhaj on his debut in 2006. He would have a number of boxing bouts in his native Italy, culminating in a fight for the vacant W.B.C. Mediterranean title, losing a decision to Nikola Sjekloca. So far, unable to replicate his success on the kickboxing circuit he would be unsuccessful in his two other boxing title fights to date, losing three fights for the Italian title in 2008 and 2010. Returning to kickboxing action in Europe, in between boxing, Cocco managed to pick up some good wins, defeating Thomas Hladky and multiple Muaythai world champion Rayen Simson to claim the Kings of Kickboxing Munich title in 2007, but dropping decisions to Yohan Lidon, Jiri Zak and Dmitry Shakuta. He lost to Yury Bessmertny by TKO due to a cut at Thai Boxe Mania in Turin, Italy on November 24, 2012. Even though the cut was caused by an accidental headbutt, Bessmertny was given the win rather than the bout being made a no contest. He lost a unanimous decision to Karapet Karapetyan at in Milan, Italy on April 20, 2013. He became W.K.N. Super Middleweight Oriental Rules Intercontinental Kickboxing Champion, facing Yoann Kongolo at Thai Boxe Mania in Turin, Italy on January 25, 2014, winning by judges split decision.
