The software reqs document for Project Server 2016 clearly states that it supports "Microsoft SQL Server 2016 RTM". But further down in the same doc under the heading of "Cube Building Service requirements", it states: "SQL Server 2014 is the supported database server for SharePoint Server 2016 Enterprise", and also: "SQL Server 2014 Analysis Services must also be installed on your SQL Server 2014 database server for your SharePoint Server 2016 Enterprise deployment if you plan to use the Cube Building Service in Project Server 2016."
So, is SQL 2014 Analysis Services required to support the project server cubes, or is the documentation out of date and SQL 2016 Analysis Services is fully supported?
I got it to work using SQL Server Analysis Services 2016 along with Project Server 2016. The trick is to install the SQL AMO from the 2014 Feature Pack on the SharePoint app server that is running the Project Service Application and then restart the Project Service Application service (or do a reboot).