Can you install SQL 2008 (Not R2) on a Windows 2016 Server?

Yes you can, as I did this last week.

Obviously SQL Server 2008 is coming out of extended support on 9th July 2019. See here.

Simply ensure you have enabled .NET 3.5 SP1 before installing SQL Sever 2008 though and it installs like a charm. Oh, don’t forget to change your firewall settings to allow applications through on port 1433 & 1434!