The jury of eight women and four men heard evidence from witnesses over seven days and retired to consider a verdict at midday on Tuesday.
Chairman of the Dilworth Trust Board Aaron Snodgrass apologised to the victims after the verdicts.
"We are deeply sorry for the hurt caused to Old Boy survivors by Mr Cave's grievous breach of trust and criminal offending when he worked at Dilworth," he said.
"We also acknowledge and regret that the safeguarding practices of Dilworth School in the past did not adequately ensure the safety of our students. This does not reflect our current safeguarding and child protection practices and other policies regarding the care, safety and well-being of Dilworth students."
He added: "The abuse suffered by some of the Old Boys in Dilworth's care is, and was, completely unacceptable."
In all, 12 people associated with Dilworth School have been charged over sexual offending between the 1970s and 2000s. Three of the accused have died, and another three have been convicted.
Cave's case was the first to go to trial.
The jury heard from a former student who said Cave grabbed his crotch in a small room off the school's chapel in the 1970s. He complained to the principal at the time, Peter Parr, but no action was taken.
Cave left the school to travel abroad but was rehired as head of the music department a few years later.
In that role, he was accused by four boys of sexual abuse during visits to his bach on Waiheke Island.
Crown prosecutor Jacob Barry said Cave's offending against the boys was strikingly similar.
"He was prepared to use his positions at schools to form relationships with teenage boys, took those relationships beyond the school environment and used disinhibiting substances to induce sexual behaviour.
"He had an interest in young, adolescent males and acted upon them in private settings."
The fourth boy told his mother about the abuse, and she reported it to Dilworth. Cave left the school soon after, though it was never referred to police.
Cave went on to teach at St Paul's Collegiate, where he was accused of abusing a student there. The student reported it to police in 2012 and an investigation was started but no charges were laid.
At the closing submissions, defence lawyer Warren Pyke asked the jury whether they could recall what they were doing 40-50 years ago.
"I doubt you can and I doubt these complainants could too. We need to remember that time does affect memories," Pyke said.
"This is an attempt to paint my client as an evil man who cannot control himself."
He accused the boys of making up the abuse, saying that one student had formulated "a tissue of lies".
Barry said the Crown's case was not that Cave touched and abused every young male that he came in contact with.
"But he plainly had a type. Every one of these six complainants knew him through a teaching relationship.
"Cave was prepared to use his positions as a vehicle to prey on young men," Barry said.
He added: "Dilworth is like an island oasis. Children are plucked from a difficult life, to strive here, yet someone like Cave has taken advantage of this."
Cave was arrested and charged as part of Operation Beverly in 2020. The police operation followed an internal inquiry by the school after it was alerted to historic abuse by a former student.
