Rubik Cube Algorithm for general n

Question

I am not sure if this is the right place , but:

Is there an algorithm for solving $n\times n \times n$ rubik's cube (non-trivial one)? If so how efficent is it? Now say I have a $n \times \ldots \times n$ ($d$ times) rubic cube , is there an algorithm that works effiecently for this case?(of course now it depends also on $d$ and not just on $n$)

I haven't found anything online/on wikipedia and I was just wondering.