The Office 2016 August 2016 updates and cumulative updates are now available, please see the links below:
https://support.microsoft.com/en-gb/kb/3181038
Project 2016 August 2016 update:
https://support.microsoft.com/en-gb/kb/3115424
SharePoint Server 2016 August 2016 update – Project Server 2016 fixes:
https://support.microsoft.com/en-gb/kb/3115437 & https://support.microsoft.com/en-gb/kb/3115441
The Office 2013 August 2016 updates and cumulative updates are now available, please see the links below:
https://support.microsoft.com/en-gb/kb/3181038
Project Server 2013 August 2016 CU Server Roll up package:
https://support.microsoft.com/en-gb/kb/3115448
Project Server 2013 August 2016 update:
https://support.microsoft.com/en-gb/kb/3115456
Project 2013 August 2016 update:
https://support.microsoft.com/en-gb/kb/3115434
Also worth noting, if you haven’t done so already, install Service Pack 1 http://support2.microsoft.com/kb/2880556 first if installing the August 2016 CU.
As always, fully test these updates on a replica test environment before deploying to production.