Universal Soldier was a 1992 action film, directed by Roland Emmerich and starring Jean-Claude Van Damme and Dolph Lundgren as two men who died as Vietnam, only to be resurrected as brainwashed super-soldiers, controlled by drugs and cybernetic implants. Like RoboCop from a few years earlier, the film could be taken as either a straight-out action gore-fest, or as something more ironic.
(The 1992 film was followed by several bad sequels, but their existence is basically irrelevant to this question.)
Apart from the film series, there is an older anti-war folk rock song with the same title. It was first recorded by the songwriter, Buffy Sainte-Marie, in 1964 and became a hit for Donovan the next year.
Google Ngrams confirms that there were essentially no published appearances of the phrase "Universal Soldier" prior to the song's release. In the (unsmoothed) year-by-year Ngram search results, it is easy to how the phrase first appears in the mid-1960s, with usage peaking in 1972; then the rate of appearances settle down to a modest level, before they begin rising agin with the release of the first Universal Soldier film in 1992.
There does not seem to be much in common (in terms of tone, or anything else beyond the fact that both are about ill-fortuned warfighters) between the song and the movie. So why did the filmmakers take the name "Universal Soldier" for their film?