Police have begun a murder investigation following the death in the early hours of Sunday.
Officers were called by the East Midlands Ambulance Service to the property in Sawley Street at 1.37am.
A man in his 30s was found with a stab wound.
He was pronounced dead at the scene, Leicestershire Police said.
A 44-year-old man has been arrested on suspicion of murder.
Another five men, aged between 24 and 53, have been arrested on suspicion of assisting an offender.
Detective Chief Inspector Tim Lindley, who is leading the investigation, said: “We believe the incident happened inside the address in Sawley Street in the early hours of this morning and sadly a man has died as a result.
“The victim and the man currently in custody for murder are known to each other and our priority at this time is to establish exactly what has occurred.”
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Police have been carrying out house-to-house enquiries to work out “the circumstances surrounding the incident”.
The street was closed off for much of the day, but the cordon has since been lifted.
Officers have appealed for anyone “who heard or saw anything that might help with” the investigation to contact them.
