You think that the 2x2x2 is simple?
Not so sure ....
When you've finished the first layer
your cube will look like this:
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If you know the 3x3x3 is exactly the same formulas except that there is no cross.
It suffices to correctly position the corners
Take a corner reference.
For example, I take the corner
white / red / green |
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To place one just to the left (white / orange / green) several cases available to you:
1) - Corner White / Orange / Green:
A- A corner to place (white / orange / green) is on the second layer:
Turn the second layer for the corner (white / orange / green) under reference.
3 cases are possible:
1 - The orange side is facing you:

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D' L'
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2 - The green side is facing you:

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D B D L'
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3 - The white side is facing you:

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D' D' F' D F
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B- The corner position (white / orange / green) is on the back:
Turn the back side (B or B') once or 2 to get the corner (white / orange / green) on the second layer.
You are now at point A.
C- The corner in place (white / orange / green) is on the left side:
Turn the left side (L or L') once or 2 to get the corner (white / orange / green) on the second layer.
You are now at point A.
The second corner positioned correctly,
your cube should look like this:
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2) - The
corner white / orange / blue:
Place the cube in the corner (white / orange / green) is on your right.
A- The corner to place (white / orange / blue) is on the second layer:
Turn the second layer for the corner (white / orange / green) in the corner that you just placed (white / orange / green).
3 cases are possible:
1 - The blue side is facing you:

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D' L
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2 - The orange side is facing you:

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D' D' L L
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3 - The white side is facing you:

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D' D' F' D F
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B- The corner position (white / orange / blue) is on the left side:
Turn the left side (L or L ') once or 2 to get the corner (white / orange / blue) on the second layer.
You are now at point A.
The third corner properly positioned,
your cube should look like this:
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3) - The corner blue / white / red:
Place the cube in the corner that you just placed (white / orange / blue) is on your right.
A- The corner to place (blue / white / red) is on the second layer:
Turn the second layer for the corner (blue / white / red) in the corner that you just placed (white / orange / blue).
3 cases are possible:
1 - The blue side is facing you:

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L D' L' F' D' F D D L D' L'
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2 - The red side is facing you:

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L D' L'
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3 - The white side is facing you:

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D' D' F' D F
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B- The corner position (blue / white / red) is located but misguided:
Just
off the corner on the second layer and place it in the corner (white /
orange / blue) to find himself in one of 3 possibilities of point A.
In the diagram below, it is possible that your corner (blue / white /
red) is not oriented such. It's not important! Apply when the same
formula!

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L D L'
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The first layer should be finished!

You can now proceed to the second layer
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