Can I purchase 3 x 2 sockets Veeam Backup Essentials and then again 3 x 2 sockets Veeam Backup Essentials for the second cluster?
Unfortunately, no. Veeam defines an organization as:
A company or any affiliates of the company, whether a separate legal entity or not, which is or becomes owned or controlled directly or indirectly, or is under common control with the company or its successor entity as to more than fifty (50) per cent of such company’s issued equity share capital, voting rights and/or the like. Organizations can span geographic locations, lines of business, domains and other organizational characteristics.
So Veeam Availability Suite is the way to go, please check this page