That was Paths of Glory (1957) and Stanley Kubrick first bigtime directing job...
Kirk Douglas came to regret it as Stanley later claimed he did everything on the film from directing, to writing, to tearing down the sets. It is a wonder Kirk did not break him in two...
Yes, Bobby Darin played Cpl. Jim Tompkins in Captain Newman, M.D. (1963) and I believe was nominated for an Oscar as Supporting Actor. Robert Duvall and Eddie Albert both had outstanding supporting parts in it.
And Kubrick even married one of the cast - the young German singer. He was a busy guy!<.P>