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With a 4x4x4 cube, it's possible to apply the same strategies as for a 3x3x3, either treating it as a 3x3x3 with a double-width middle or else as a 2x2x2 and just working on the corner "quadrants". Centres of each face can also be handled as a 2x2x2 cube, ignoring the outer layers entirely.

Is it better to apply those strategies in one order rather than the other?

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Notation
We need to have some notation for the algorithms. We use:

  • $U$ for the upper layer and $u$ for the middle upper layer.
  • $R$ for the right layer and $r$ for the middle right layer.
  • $L$ for the right layer and $l$ for the middle left layer.
  • $F$ for the front layer and $f$ for the middle front layer.
  • $?^2$ for turning a layer twice
  • $?'$ for turning counter clockwise

Example: $(Uu)^2 ~ l'$ is turning the upper half of the cube twice and turning the middle left layer counter clockwise.

Solving
Note that you need the same colours as on the 3x3x3, but with the 4x4x4 you can mix them up and later on while solving you have a problem when yours centers doesn't have the same colours as the 3x3x3. So it easier to reduce to a 3x3x3 than a 2x2x2.

  1. Solve the centers, by bringing two times two pieces together and then bring those pieces together and you have a solved center: (this can mostly done by intuition)
    • White Up, Red Front, Blue Right,
    • Yellow opposite to White
    • Red opposite to Orange
    • Blue opposite to green
  2. Solve the edges (watch the video linked below and this becomes intuition)
  3. Solve it as a 3x3x3
  4. Solve the parities:
    • Edge parity: you want to flip one edge. $r' ~ U^2 ~ l ~ F^2 ~ l' ~ F^2 ~ r^2 ~ U^2 ~ r ~ U^2 ~ r' ~ U^2 ~ F^2 ~ r^2 ~ F^2$
    • Corner parity you want to swap two corners. $U^2 ~ r^2 ~ U^2 ~ r^2 ~ (Uu)^2 ~ r^2 ~ (Uu)^2$
      Note: Actually you swap two edges, so you need to do some more solving after you have performed this algorithm.

  5. Finish the cube and profit!

    Corner parity and edge parity

Edge parity Corner parity

And I want to show you a good YouTube tutorial. (in this video he never mentioned a 2x2x2, but he did find it necessary to master the 3x3x3)

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    $\begingroup$ I'm not sure the question was asking for what the general method is, actually (though this is a good listing of a general method) - I read it as though it's asking whether it's better to reduce to a 2x2 or 3x3. $\endgroup$
    – user20
    May 25, 2014 at 17:51
  • $\begingroup$ The corner parity algorithm here certainly doesn't work. I didn't test any of the rest ... $\endgroup$
    – hippietrail
    Jun 29, 2014 at 1:12
  • $\begingroup$ sorry, I fixed it $\endgroup$
    – martijnn2008
    Jun 29, 2014 at 8:04
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the strategies mostly used are to solve each of the 2x2 faces (and positioning them) then the edges and then you can treat the entire cube as a normal 3x3x3

the key algorithms are 2R U2 2R' that is move the right part of the front face to the top rotate it and then move the new part back, this will allow you to solve the center faces

the other one is 2B R U R' 2B' or rotate the bottom 2 layers splitting up the edge, moving the top part of the split side up, rotating in a new edge and moving it all back again. This will allow you to solve the edges.

after that is it just a clunky 3x3x3.

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    $\begingroup$ Not entirely true, you can have two sort of parity. Edge parity and corner parity both of them are not in the 3x3x3. $\endgroup$
    – martijnn2008
    May 25, 2014 at 8:25
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The 4x4 solving strategy is quite hard ,since there are lot of parities that can occur with the dedge type of pieces.

The top solvers today use the method of Yau , and Hoya to solve a 4x4. I have a video explaining the Hoya method , right here, Hoya Method

There are some ways to avoid parity but it is quite advanced level, 4x4 parity avoidance

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