This is a pretty bad premise. If you're packing people in cubicles in a building/floor that most likely uses central air and air conditioning, you already lost the game -- sphere packing or not.
Indoor HVAC air flows seem way more important than distance. I can probably sit right next to you as long as the airflow has each of our exhalations taken away from the other.
My employer has mentioned potential plans to bring people back to the office in small numbers for short times. Until these discussions include analysis of building HVAC, I want no part of it.
Packing spheres might help prevent some transmission, but based on other reports, HVAC flow is a contributor. You can have everybody sitting 10' apart, but if the air moves consistently in one direction, anybody stuck downwind of a typhoid mary runs a high risk of infection.