Closed loop system for a system this big and hungry would demand many km^2 of radiators with a forced air-flow. Look at your A/C external unit - it's barely handles 10-15C degree difference for a small room and that is for a human with a measly 300-500 BTU/h. A typical server is 2000 to 6000 BTU/h, depending on the configuration and a typical 42U rack would have at least 10-15 servers, not counting TOR switches and other shenanigans.
The hydrological cycle is already a closed loop system. The water you drink today watered a plant 10,000 years ago, passed through Abraham Lincoln's kidneys, or was drank by Genghis Khan.