I've seen people misidentify the octaves before on this type of question, so be certain that you have the correct notes (C6 is the "Soprano High C", and should sound really high). If you have the correct octave numbers, proceed.
It's definitely not impossible for males to sing C6. Michael Jackson in Smooth Criminal, anyone? Prince? Freddie Mercury's done it as well. There are more examples than just them, of course, and amateur singers sometimes have that note as well. Plenty of regular males can in fact go there and higher, and I know one who can.
He can sing C6 pretty much on command, and at his highest ever, he's sung C7. He says that while he's not sure whether anyone can hit C6 with practice, it certainly can't hurt to practice falsetto a lot as long as you're not doing something wrong.
He and every other (post-adolescent) male I've seen who can do it (and for that matter, females) use falsetto to get up that high. He also says that he notices that he tends to be able to go highest when he's excited, such as on a rollercoaster or cheering in a crowd, so perhaps adrenaline helps. In my very limited experience, the males who can do that up that high tend to be baritone voices, but I doubt that that's a hard-and-fast rule at all. (There's also a phenomon called whistle register, but that apparently is even more ridiculously rare for males).
It's always tricky advising people on how to extend their vocal range. The thing I usually recommend would be to practice (and make sure you're not injuring your voice, as always!), and consider finding a vocal instructor. I find that the more one sings in falsetto, the easier control gets, and usually the easier it gets to produce the higher notes.
One final note: The extremities of the male falsetto range can sound very unpleasant if done without control, and that's a common issue with the male falsetto register in general. It's rare nowadays to hear a male singer with such control over the extreme high range of his falsetto as to be able to use it musically (in fact, it's uncommon for female singers too).