Paul Newman is Rocky Graziano in this biopic. Also starring Pier Angeli, a young Robert Loggia (It took some time before I recognized him) and Steve McQueen in a small part, directed by Robert Wise.
It's a bit hard to get past Newman doing an Italian/NY east side accent, there weren't any Italian actors around?, but it's a decent film. It's the Hollywood version of Graziano's autobiography, so who knows how much of it is true. It's a pretty traditional rags to riches story, ending in triumph, giving the filmmakers a lot less freedom. I prefer Wise's earlier boxing picture The Set-Up.