Cavan was jailed for life in 2013 for murdering defenceless David Corr in his New Lodge Road flat the previous year.
He claimed he carried out the brutal stabbing Mr Corr, a busker, was playing loud music in his flat.
A judge told Cavan he would serve 13 years in jail without parole.
In a statement, the Prison Service said the man’s next of kin have been informed.
It is the second death at Maghaberry in less than two weeks.
Remand prisoner Gerard Mulligan took his own life on November. He was awaiting trial for murdering his father Gerard Mulligan snr in Lisbur.
DAVID CORR MURDER BACKGROUND
Barry Cavan, from Cuchulainn House in the New Lodge area of the city, admitted the murder of David Corr on 15 March, 2012.
The body of Mr Corr, who was also from the New Lodge area, was found at his flat in Victoria Parade. The 24-year-old had been stabbed to death.
Cavan was told he had committed a “brutal, senseless killing”.
Mr Corr, also known as Dee, was a talented skateboarder and busker.
Belfast Crown Court judge Mr Justice Weir said that while Cavan had had a dispute with Mr Corr over the playing of loud music, that could not “begin to explain, never mind justify” the killing.
He emphasised to Cavan that even when he has served the minimum 13-year period, it would be up to the parole commissioners “if and when” he will be released and under what licence conditions.
The judge also told Cavan that the life sentence he was obliged to impose meant that he would forever be liable to be recalled to jail if he breached any of his licence conditions.
Cavan had pleaded guilty to murdering Mr Corr on 15 March 2012.
He sustained 39 wounds in the frenzied attack and while it was a stab wound to the chest that caused his death, many of the injuries he suffered were to his arms and hands.
Cavan, who lived in the flat above his victim, called police himself and told the 999 operator he had killed his neighbour after stabbing him “30 or 40 times”.
When officers rushed to the scene, Cavan was lying face down prone on the hallway floor and confessed immediately.
Mr Justice Weir recalled Cavan had been complaining for three months about the volume levels his neighbour played his music at in the early hours of the morning, complaining to his neighbour, the flats caretaker and Belfast City Council.
He had also told a friend, known only as ‘S’ that he was thinking about stabbing his neighbour.
On the night of the murder Cavan, who had consumed about seven litres of cider had called into his neighbour’s flat about three hours before he launched his attack. He had a kitchen knife with him then.
The judge told the court how Cavan had texted a friend “I’m in his flat now, kitchen knife in pocket” and ‘S’ had told him to get out.
Mr Corr told him he would use headphones to listen to music in future, and Cavan left.
Three hours later Cavan returned to the flat and Mr Justice Weir described how the men were on the sofa.
Cavan “began stabbing him and continued, despite his pleas and screams, to stab and cut him”.