It is thought that two men forced their way into the home. Police were called shortly after 9pm and discovered Mr Adams on the ground outside with serious injuries.
He was taken to a north London hospital but he was pronounced dead at 11.56pm.
His next-of-kin have been informed and a post-mortem examination is to take place.
Detectives from the Homicide and Major Crime Command, led by Detective Chief Inspector Noel McHugh, are investigating and are appealing to witnesses or anyone with information to get in touch.
Mr McHugh said: “Tragically a man has lost his life in what appears to have started as an aggravated burglary and ended in his death, after he fell from a third-floor window.
“It is very early in the investigation, but I believe two men forced their way into the flat armed with at least one knife.
“This appears to be a targeted attack and there will be people out there who will know who is responsible for the events that led to Sheiku’s death. I need to hear from those people as a matter of urgency.
“We need to understand the circumstances as to how Sheiku came to fall out of the window and we are appealing to any local residents who saw two men loitering around the area before 9pm to come forward.
“We will be working around the clock to piece together the circumstances of this case and bring those responsible to justice.
“What we need now is for witnesses and people with information to do the right thing and contact us as a matter of urgency.
“Any information, no matter how insignificant you think it is, will be treated in the strictest confidence and will assist us greatly in this investigation.”