I tried to load service pack 3 for 2016 and was not able to initially. When I first started the Installation Manager, I encountered an error message telling me that a reboot was pending from a previous installation. (This wasn't true, by the way as I just installed 2016 last week and I'm positive that I did restart immediately after installation.) It was recommended that I cancel the sp3 installation and reboot now. I did.
Then after a reboot and a fresh cup of tea, I started the Installation Manager again. This time I got a different error message telling me that an HTML file could not be created. Cause . I was told to contact my local support representative, so I did. He had never heard of any of these messages and told me to just press `OK' and see what happened. I did that and now am downloading the service pack files. Whether I am successful fully installing sp3 remains an open question.