Yes, I can. It takes me four minutes on average, but my fastest time is two. I can perform the algorithms without looking at the cube (but don't expect me to solve blindfolded or behind my back).
I can also solve the Professor Cube (5x5x5), but I rarely do since it takes me at least half an hour to do so, but I can't solve the 4x4x4 (I haven't gotten one yet, so I technology have not solved it yet.
I love to see people's reactions whenever I solve it.
-I can't stand those things.
-Did you just solve that?!
-You cheated, didn't you?
-You can solve that, too?
And the list goes on.