“I’m so young and you’re so old,” Paul Anka sang in the very first line of his very first hit, “Diana,” in 1958. It’s the kind of lyric you could seemingly only get away with when you’re 15, as Anka was at the time, and maybe not a minute later, or at least not much past the point when the goddess you’re singing to is not that much farther along into her teen years. Remarkably, Anka still has that debut smash in his concert sets today, and it’s a moment for a mass sing-along, not mass cringing — maybe partly out of irony, but also because, at 84, the singer really does seem young at heart, to borrow a phrase from his most legendary buddy.

This week sees the home-viewing premiere of an HBO Original documentary, “ Paul Anka: His Way ,” picked up by the cabler/streamer after a run on

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