"They put me through the wringer," the budding star, 24, tells PEOPLE of his audition process.
"For two years I was going to acting classes, learning techniques, going to auditions, callbacks, and things like that," he adds.
His father, meanwhile, wanted to make sure he got no special treatment.
"I knew that people would think I just gave him the job," Ice Cube (who was born O'Shea Jackson), 46, admits. "So I wanted him to be more than ready. I wanted him to be a great actor by the time we started to shoot."
To prepare, Jackson Jr. trained for months with acting coaches including Aaron Speiser, who works with Will Smith and Gerard Butler, and Susan Batson, who works with Nicole Kidman.
Adding to the already intense pressure of being a first-time actor in a major film, Jackson Jr. was determined to represent his dad accurately onscreen.
"When you haven't acted before, it's a big dish," Jackson Jr. says. "But I couldn't sit in a theater and think someone is portraying my father the wrong way. If I was thinking 'Oh, he wouldn't have done that' it would've nauseated me."
Ice Cube: The Sexiest Guy in 22 Jump Street!
But even after years of hard work, when it came time to cast the role there wasn't any room for nepotism.
"If we found a better Cube, then we had to go with the best man for the job," the N.W.A co-founder says. "That's how acting and movie shoots work. So I couldn't give it to him – and I wouldn't if I could because that's easy."
The decision came down to the wire. "When we got to the chemistry test, there were two other Cubes and three Dr. Dre's, so the competition was on," the actor remembers.
Ultimately, the choice came down to something other than his appearance and acting skills. The goal for Straight Outta Compton was to have the actors re-record the classic N.W.A album of the same name, and use their real voices onscreen. Jackson Jr., who was an aspiring rapper before casting began, finally sealed the deal with his skills on the mic, a production source reveals.
"When Universal finally picked me it was a weigh off my shoulders," he says. "And making me do all that work built confidence."
His dad couldn't have been prouder. "It's amazing. I can only equate it to a guy watching his kid win the Super Bowl on the same team he won the Super Bowl with," Ice Cube says.
"He did a phenomenal job," he adds with a smile. "I don't know if I could've done a better job playing me."