First, you must make a "Sonobe Unit". You will need six of these to make a full cube.

Take a square piece of paper. If you are using colored origami paper, flip it so it is colored side down.

Step #2

Fold the paper in half horizontally.

Step #3

Unfold the paper. You should have a horizontal crease in the middle.

Step #4

Now you are going to fold the paper in fourths.
Start by folding the top down to meet the crease in the middle.

Step #5

Fold the bottom up to meet the crease in the middle.

Step #6

Unfold the top.

Step #7

Fold the bottom corner up to meet the upper crease.

Step #8

Unfold the paper completely.
Rotate the paper Upside Down (180 degrees).
Fold the bottom flap up to meet the middle crease.

Step #9

Fold the bottom corner up to meet the upper crease.

Step #10

Fold the top down.

Step #11

Refold the top-right corner down along the previously formed crease.
Tuck it into the bottom flap.

Step #12

Turn the paper over.

Step #13

Fold the corners over

Step #14

Turn the paper to the right, so the right-side becomes the bottom-side.
Fold the corners in to form a square.
First one corner,

Now the other corner.

Step #15

Flip the unit over.
It is complete. There should be two triangular pockets that you can use to insert other units into.

Step #1

Insert one Sonobe unit into the pockets of another unit.

Step #2

Insert another Sonobe unit.

Step #3

Now fold the squares together to form right angles and connect the units.
You should have 3 faces of the cube and one corner.

Step #4

Continue forming the cube.
It should look like this before inserting the last unit.

Step #5

Insert the last unit.
You are now finished!
It should look like this.

Here is a finished cube using color paper.