The common assumption among non-cubers is that the bigger the cube becomes, the harder it becomes, however, this is really not the case as larger cubes usually just follow a similar method to their smaller cubes. For example, anyone who can solve a 6x6x6 should be able to solve an 8x8x8 and 9x9x9 and any larger cube, it will just take an increasingly longer amount of time. Ultimately a larger cube taking longer to solve does not make it harder, it just means that it takes more moves to solve and for some people a long solve of a large cube can be very enjoyable and really not that challenging. Similarly when you start going into large minx puzzles such as the teraminx and petaminx, these puzzles are not especially hard, there is not even any parity, if you can solve a megaminx and a 7x7x7 then you can solve a teraminx, it will just take a very long time. Larger cubes also have more possible moves, for example, if you were to dismantle a 3x3x3 and randomly reassemble it there would be a 1/12 chance it would be solveable, however, if you dismantled a 4x4 and randomly reassembled it then there would be a 1/3 chance it would be solveable.

So what is actually harder? To make a harder puzzle you need some sort of bandaging to prevent certain moves from being possible, this makes things a lot more difficult because most speedcubers work by doing various algorithms to do certain steps, a banaged cube can frequently provide a situation where a solver does an algorithm and then abruptly has to stop part way through because the next move is impossible. Some people will make their own bandaged cubes by using a colour brick cube and attaching longer bricks on certain sides to make it harder, while some manufacturers have produced various bandaged cubes. Probably the hardest cube I stock is the puppet cube version 1, this cube is incredibly hard because so many moves are restricted and there are inner pieces which you have to get correct too, I am not aware of anyone in the UK that knows how to solve it, although I do hope to find someone??? Harder cubes are definitely possible but have not really been produced because there isn't that much demand for them.