Another name is water bomb.

Fold a square sheet of paper at the diagonals and unfold it. Put the paper at both arrows together. Lay the triangles at the top and at the bottom on top of each other.

The result is a flier triangle, which is known from the swallow or the pigeon.

Fold upward on the red line on the right and on the left.

Then it must look like this.

Fold on the red lines.

Then it must look like this.

Fold the two little triangles on the red lines downward.

Put the last made triangles in the two pockets on the right and on the left. This is a little bit fiddly.

Then it must look like this.

Turn the whole triangle and repeat the steps 3,4,5,6,7,8,9.

Then it must look like this.

Fold and unfold on the red lines.

Take the folded cube in hand and blow into the hole at the top. Unfold the cube by this.

The cube is ready.

Some Mathematics   top

If you take the cube apart, you get a nice pattern, which is made by the folds.   You find the formulas: .........

On the left you can see the largest net of a cube, which fits a square. You find the formulas: This cube is much bigger than the folded cube.

See more in book (5), Seite 63f. und Seite Seite 71ff.  "Der eingewickelte Würfel".

Origami Cube on the Internet 

Englisch:

Dr Stephen O'Hanlon (Ring of Origami Art)
Water Bomb  (  .pdf file)

H. B. Meyer (Polyeder aus Flechtstreifen)
Cube 

Malcolm Goris 
Instructions to Build Water Bombs

Puzzle Playground  (Puzzle_com)
Square to Cube

H. B. Meyer (Polyeder aus Flechtstreifen)
Würfel

Jennifer's Puzzle
Flechten eines Würfels aus 3 Streifen

zzzebra
Wasserbombe

References    top
(1) Joachim Schönherr, Wir falten und falzen, Leipzig 1990
(2) Therese Mielhaht: Origami Spaß mit Papierfalten, Köln 1990
(3) Kunihiko Kasahara: Origami - figürlich und geometrisch, München 2000
(4) Kunihiko Kasahara: Origami - ohne Grenzen, München 2001
(5) Martin Gardner: Mathematische Hexereien, Berlin/Frankfurt am Main/Wien 1988 [ISBN 3550065787]