Cuban issued the strongly-worded response after 59-year-old Nelson made the allegations in a lawsuit filed in Dallas County.

In the suit, Nelson said his nephew was interested in getting a job in sports and entertainment -- and went to interview with Jason Lutin, Cuban's chief of staff with the Mavericks, about openings in the NBA team's org in 2020.

Nelson claims the two talked while out at lunch during a work trip in Chicago -- when Nelson says Lutin asked Nelson's nephew to go back to his hotel room to talk further.

In the docs, Nelson claims that's where Lutin sexually harassed and sexually assaulted his nephew.

Nelson says his nephew notified the Mavs of the incident ... but claims Cuban swept it all under the rug, insisting Cuban bought "his way out of the problem."

Nelson added that when he learned of the alleged incident months later and brought it up to Cuban and others in the org., Cuban and the Mavericks asked him to sign a confidentiality agreement and remain quiet about it all.

Nelson claimed Cuban wanted to silence him "so the Mavericks could hide from the public and the Mavericks' employees that the Mavericks were allowing a sexual predator to continue working for the Mavericks." He added that he believes he was eventually wrongly fired over it all.

In a statement to ESPN on Thursday, Cuban insisted none of Nelson's claims were true, saying, "Everything in that filing is a lie."

"We did multiple complete investigations and the only person that did not live up to the standards of the Dallas Mavericks was Mr. Nelson," Cuban said. "He was fired as a result. He was well aware of the investigation. He refused to fully participate. I will say it again, everything he said is a lie."

Lutin also denied the claims in a statement.