Intro | 1st layer | 2nd layer | 3rd layer | Tricks | The other methods

For the second layer, turn the cube upside down, like this:

Now we are going to take advantage of the fact that we have left one empty corner to quickly place 3 edge cubes of the 2nd layer.

Here are the 2 very simple and symmetrical movements which will allow you to do it (turn the cube in order to see well if necessary):

R U' R'

L' U L

Put 3 edge cubes of the 2nd layer this way.
Now the cube looks like this:

Turn again the cube upside down and place the last corner of the first layer. Proceed like you did for the first corners you placed, but being careful not to unfortunately remove one of the 3 well placed edge cubes of the second layer.

Now you'll have to use one these 2 algorithms (symmetrical) :

D' R' D R D F D' F'

D L D' L' D' F' D F

You have now completed the first two layers if everything went well.

3rd layer

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