The US actor, who reprises his starring role as Tony Stark/ Iron Man in the third instalment of the superhero series, admitted that the group would hire out a cinema so they can catch the latest releases.
"It was a group of us going to the Cineplex and blocking out a theatre on the weekends and taking in (cinematographer) John Toll and taking in sometimes a ton of people and sometimes less. We do something that involves movies and our love of movies," he told Entertainment Weekly.
"One was the Wachowskis' film Cloud Atlas. We were impressed with how cohesive the direction was, and obviously everything that John shot was amazing. We saw Flight, which was great, and before that it was Argo, which was also kind of cool."
The 47-year-old added: "It's nice knowing that you can go to the theatre every weekend and see something good. And it's great to see what people are doing and to get excited about it."
Robert also revealed that Don Cheadle's character Rhodey will have a bigger part in the upcoming film, which is due for release in May.
"Rhodey is much more in the dead centre of things. He's much more dynamic," he explained.
"We've made this decision that while Tony is a technical guy, he's not really a trained guy. There's a lot of fun to be had with Don because he's really good with hardware and he's a martial artist, so it's been really fun exploiting this possibility... So there's a lot more fun and a lot more depth to Rhodey this time around."