In order for you to be able to finish the cube, you will need to be able to solve a 3x3 cube, but being able to solve a 4x4 cube would also enhance your abilities for it, since the algorithms can be used on both.
If anything is unclear, just ask and I can clarify it for you
1. This is a LONG INSTRUCTABLE. It will take time and effort to get through this cube, and you need to have some free time to solve your cube.
2. I am Canadian, so deal with the u in colour.
3. I am assuming you have a 5x5 cube. If you do not, they cost up to $40 CAD, so be prepared to spend a little bit of money on it.
Step 1: My collection/experience
I can solve all the puzzles you see here, no instructions.
I found out how to do this by watching a long youtube video tutorial about how to solve this, and read some text instructions. I have 2 5x5 cubes, a few 3x3 cubes, and the 4x4 cube.
Step 2: My solve
By the way, that cube is not the one I am using in my instructions, its the Rubik's one.
Step 3: Getting started
Step 4: Notation
' means counter clockwise.
I always solve my cube white centers first, then yellow, and the rest vary. It might help to follow how I am solving it if you start on white, then go to yellow, and work with my sides.
Step 5: Getting a 2x1 block on the side of your choice
Step 6: Make a 2x2 block
Step 7: Finishing the first center
Make a 1x3 block with the remaining white pieces, but don't mess up the white 2x3 block in the process!
Try to use the side that has no white blocks on the 2x3 block, and form that 1x3, and insert it.
Step 8: Working on the opposite center
Step 9: Finishing the center.
If you have the sides like they are in the first picture, then do the following:
Dd' Uu L2 Dd Uu'
It should now be a 1x3 block
Now, align it as in the second picture, and do the following algorithm:
Ll' U2 Ll
This completes the second center.
Step 10: The third center!
Create a 2x1 block on a different side, and join it to the other one, that should have the center connected to it. It's just like solving the first center, just it's a bit easier to find the pieces. I forgot to take pictures, but I have put in the photos from steps 5-7 in, so you know it's the same thing.
You won't mess up the completed centers if you hold the cube so that the white center is in your right hand, and the yellow center is in your left.
Step 11: The fourth center!
Now, solve it like the second center, and then you have completed 4 of the 6 centers!
If you have a stray piece on your cube like in the picture, then do the algorithm used for putting the 3x1 section into the center, but make sure no greens go in!
Step 12: The final two centers!
Using the algorithm for moving those pieces around(Ll' U2 Ll), get as many of the colour on its respective side. In my case, I am getting as many blues on the blue side, and reds on the red side as humanly possible. The inverse also works, and on the right side. Possible algorithms are:
Ll U2 Ll'
Ll' U2 Ll
Rr U2 Rr'
Rr' U2 Rr
If you have a case like in the second photo, you need to get the red center on the red side, and the blue center on the blue side. Then, align them as shown in the picture, and perform this set of moves:
r U' M U r' U' M'
(M is the middle, rotate it in the same direction as R)
You may need to repeat this multiple times to solve both parts, but after they are solved, we move on the the most time consuming part of the cube: Pairing
Step 13: Pairing
Find 2 edges that have the same colours on them, and arrange them like in the picture. I turned the layer with the edge on it so that it is one photo instead of 2
Now, to pair these edges, we find an unmatched pair in the top face. Rotate the cube as much as you like, you barely have to worry about messing up the centers anymore. For the following case, you need to perform the following (It's all logic, I'm just giving you algorithms to make it easier.):
(Uu) L' U L (Uu)'
The U can be replaced with U2 or U' as well
The logic method:
Move the cubie into position, swap it with an unpaired edge, and return the centers to the completed state.
Make sure that all the center edges are facing the same way as the outer edge pieces
This will work until you have 2 edges that are not solved.
Step 14: Parity Errors
(Ll)' U2 (Ll)' U2 F2 (Ll)' F2 (Rr) U2 (Rr)' U2 (Ll)2
This can also be used in solving the 4x4.
Just arrange the cubies so that they are in that manner, and you can get it to have sections like a 3x3, and solve it. You may need to repeat that algorithm a few times.
Step 15: Done!
If you have any questions, problems, comments, or critiques, post them as a comment below.
Also, if you need more photos, I will make some more. I don't know that they will be exactly the same, but the photos I took were very minimal. If you need help solving it like a 3x3, I am working on an instructable for that next. ( Don't worry, I have a newer cube than the one in the photos )