The actor, writer, comedian and rapper Donald Glover is sitting in an agreeable room in the Four Seasons hotel in Manhattan. In front of him are a steak about four inches thick, a few sprigs of broccoli and a litre of expensively bottled water. To his left sit a Macbook Air and an iPhone, both charging, the latter pinging every minute or so, heralding the arrival of a new message. It would be fair to say the 27-year-old Glover has a lot on. Indeed, he's had a lot on ever since he graduated from his creative writing course at New York University five years ago.

Glover has written for The Daily Show and 30 Rock, in which he also appeared. He is part of the sketch team Derrick Comedy, whose YouTube clips have accumulated more than 30m views, nearly 9m of which are for a sketch about "bro rape". He has a wildly successful standup career and stars as Troy in the hugely popular sitcom Community.

But last night, Glover appeared before a crowd of 2,500 as Childish Gambino, a rap alter-ego that allows him to write the sort of brutally sharp lines about race, class, gender and sexuality that would never make it into a mainstream TV show. Glover calls it Black Rock.

"I'm influenced by LCD Soundsystem as much as Ghostface Killah," he says. "A lot of the rap shows I saw as a kid were boring, but if you went to a Rage show or a Justice show, the kids were losing their minds. Kids just want to go nuts, Odd Future know that. People want to experience something physical."

As Gambino, Glover can explore his every behavioural tic, trait and hangup, as well as let great shafts of light on to everyone else's. In this guise, the TV star is just a "nerdy-ass black kid", a "well-spoken token". On the song Backpackers, he concludes that as a "black male in short shorts, I'm double suspect". A nagging lyrical firefight rages across his new album, Camp – a title guaranteed to raise hackles – with Glover/Gambino being too black for the white kids he went to school with ("I hate it there, they make fun of my clothes and wanna touch my hair"), but not black enough for hip-hop, "Rap is for real blacks," a voice declares at one point. "I hate that fuckin' faggot, man."

Glover started rapping eight years ago, in an attempt to reclaim a corner of an industry that had decided only one type of expression was allowed, since when he's made a series of mixtapes and downloads before Camp, his first official album. For a few years, if you weren't a thugged-out gangsta, you simply didn't exist in hip-hop. "Rap used to be silly and now it's sillier than ever and I find that idea very freeing," says Glover, "After Tupac and Biggie died and Jay-Z took over, there was this idea that you had to be from the streets to be a rapper – people like the Pharcyde and KRS-One just disappeared. You had to be a hustler, and I'm no hustler."

"A hip-hop manager I know has this theory why Kanye West blew up when he did," he continues. "50 Cent had gone to the absolute pinnacle of thuggishness. He had been shot nine times. He had a slur from the shootings. He was huge. No one could ever be thuggier, so people reacted like they always do and went all the other way. Suddenly Kanye is a huge pop star."

A black male rapper with, to all intents and purposes, a handbag and glasses – whatever next?

"That's it exactly!" Glover shouts. "He had a bag, a leather bag! What the hell is he carrying in there? The whole of rap had become so codified that even tiny things like that would throw people off. It's funny because black guys love all that stuff, but no one was talking about it because it wasn't allowed."

So why does black popular culture have such a problem with even the suggestion of homosexuality?

"Dude, I've spent a lot of time trying to figure that out," he says. "Black men struggle with masculinity so much. The idea that we must always be strong really presses us all down – it keeps us from growing. Black culture is a fight. We want to hold on to what we are, but sometimes the things that we are can be totally negative. You have to think: can't we try something new and not be seen as suspect? Can't we hear the n-word someday and not be upset? If a black person called a white person the n-word, would that help a little? We're fucked up. It's a fucked-up situation, but I have to address what's there."

But do you really think a pop record could ever affect change in something so entrenched?

"It can try," he says. "For along time music was black or white, but now there's people like Tyler the Creator making a huge impact. Like me, he's a middle-class black kid that dressed like a member of Good Charlotte and got called a faggot. I got jumped once simply for having a skateboard. We need to change the norms. I can't wait till there's an Asian rock group, and kids can't tell the difference any more."

Glover grew up in Stone Mountain, outside Atlanta in Georgia. The KKK enjoyed their second revival there a century ago, and Martin Luther King Jr namechecked it in his I Have a Dream Speech. Its greatest claim to fame is carved into the face of the huge granite outcropping that gives the town its name: the world's largest bas-relief.

"It is a very segregated place," he says, "but I loved living there. The mountain itself is like a granite pimple on the ass of the earth, and just to rub it in, they've carved a group of Confederate leaders' faces into the rock. The land right next to the mountain is full of old white people who will never move, but around that it's a very suburban black area."

His parents ran a daycare centre and also adopted and fostered other children, and Glover insists his creativity is informed by all the sadness and humour he soaked up at home. As a teenager, he'd deliberately scare himself by listening to Eminem's Kim – a song full of fantastically violent, murderous imagery. "That song showed me the dark scariness that lives inside everyone," he says. "My parents were convinced listening to that music would make me become a devil worshipper. I still feel rappers aren't given a chance to say that these are just feelings. It's not right, but humans feel that way sometimes. I think it's odd that you can't joke about rape, when people joke about murder all the time. A lot more people are dying than getting raped. I think it's a comedian's job to make everything funny. Nothing is off-limits."

What did you make of Ricky Gervais's "mong" remarks then?

"If you take risks, you face the possibility you might fail," he says. "But I believe the perfect joke would turn someone. My sister has mental problems, but I use the word 'retard' in my comedy. Do I love her any less? Would I go up to a mental ward and say: 'You're idiots'? No. I would never do that, but sometimes saying retard is funny, it's a release."

Ultimately, the problem Glover faces is the same one faced by Lenny Bruce and Richard Pryor and Chris Rock before him, as well as Gervais right now, and that is: who is that laughter a release for? Is he kicking up or down?

"I don't know the answer to that," he says. "I know people are right to complain, but those kids who say 'mong' or 'retard' won't stop saying it, just because a comedian does. I say the n-word and I try and use it cleverly, but people will still get hurt. People still call me faggot, because I wear tight jeans and don't like the stuff black guys are meant to like. The truth is I'm a grown man, and I still remember all the shit that happened to me. Childish Gambino is about facing the fact that none of us really get jaded or grow a thicker skin – we just shy away from what originally hurt us. We bury it. I know I carry around all my collected hurt with me everywhere. I also know it made me who I am."