My limited understanding is that both SAS 9.x and SAS Viya 3.x can be installed on premise or in third party data centres. Viya 2020 and 2021 are available on MS Azure which is only available at MS data centres (happy to be corrected on this). SAS is working on Viya 2021 versions that will run on AWS and other cloud platforms that can either be on premise or third party data centres.
As has been pointed out in the thread, SAS Viya 3.x is indeed supported for deployments on-premises (and in the cloud), just as SAS 9.x is.
The latest version of SAS Viya, colloquially referred to as "SAS Viya 4" and technically referred to by its continuous delivery release numbers [i.e., LTS 2020.1 (released in November 2020), LTS 2021.1 (May 2021), Stable 2020.1.x (monthly releases through April 2021), Stable 2021.1.1 (May 2021)] is currently available for public cloud deployment. As of LTS 2021.1, that includes Azure, AWS, and GCP. SAS is targeting delivery of an on-premises option based on OpenShift running on VMWare this summer.