It's not really broken (in fact almost new)
but I want the pieces to move faster
At a guess, without having seen it, I'd say you may have possibly put too much lube into the cube, and its having a slow effect to start. You could either clean out your cube(cold water with some alcohol gets rid of the dirt but be careful) and then re-lube it, or just try playing with the white side a lot. R U Ri Ui seems to be an easy way to loosen it up. But that is only my suggestions, don't take them for gospel-
What's a silicone grease? How does it differ with normal silicone spray? Is that what syuhei uses to lube his eastsheen?
Who is Syuhei?