can we install air cooled ac system in lower basement to cooler the entire building and how it works?

Answer 1

air cooling and air conditioning are different systems...

if you mean AC system then i think it can not be installed in the basement... they should be outdoors... the system generates a lot of heat...

Answer 2

Air conditioning systems can be either air-cooled or water cooled ; it depends upon which heat rejection medium passes through the AC unit condenser. AC systems can employ either self-contained components in a single unit or they can be split-system with the heat absorbing cooling section at one location and the heat rejecting condenser section at another.

If you are going to cool an entire public building (of unstated size) you need to consult with a licensed Professional Engineer who specializes in HVAC applications in your State.

But if this is a "small" private building, you can put a self-contained air -cooled unit in the basement and run supply and return air ducts to it. However, the heat removed from the spaces upstairs will be rejected into the basement. You can cool the upstairs until the basement gets too hot and the safety controls on the unit will shut it down. This arrangement could work to provide temporary cooling.
If you can arrange to have outside air furnished to the basement to remove the heat, the system will work better.