Looked it up. Believe you are right = Nothofagus sp. "Southern Beeches" Bits of southern Chile, Australia, some of New Zealand and Papua New Guinea.
Group of 30+ species. Lots of strange, introduced things get planted in parks. Now that you've found one, what others are not quite recognizable?
I've met landscape architects that like to do parks that way = kind of a silent botanical garden when you know what you're looking at.