The teenager is not the only one who has climbed onto the building, but to Mr Cooper's knowledge, he is the first to have fallen.
Mr Cooper said it was an ongoing problem with young people climbing the building and throwing cans and smashing the glass verandah.
"It's very expensive. Two panes costs $880."
Five glass panes have been broken over time, Mr Cooper said.
The building is attractive to climb. It is known as criss cross castle colloquially, or the X building.
What the climbers don't know is that moss grows on the concrete, and in the dark it cannot be seen.
"It is slippery and very dangerous," he warned.
A staff member of one of the building's tenants, Montgomery Watson Harza , said they saw climbers on the building all the time.
"We tell them to get off but it falls on deaf ears."
Mr Cooper said the police were concerned and were patrolling the area, and there is CCTV that films the climbers' activities.