The Soma cube is a solid dissection puzzle invented by Danish polymath Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg.

Seven pieces made out of unit cubes must be assembled into a 3×3×3 cube. The pieces can also be used to make a variety of other 3D shapes.

The pieces of the Soma cube consist of all possible combinations of three or four unit cubes, joined at their faces, such that at least one inside corner is formed. There is one combination of three cubes that satisfies this condition, and six combinations of four cubes that satisfy this condition, of which two are mirror images of each other (see Chirality). Thus, 3 + (6 × 4) is 27, which is exactly the number of cells in a 3×3×3 cube.

The Soma cube was popularized by Martin Gardner in the September 1958 Mathematical Games column in Scientific American. The book Winning Ways for your Mathematical Plays also contains a detailed analysis of the Soma cube problem.

There are 240 distinct solutions of the Soma cube puzzle, excluding rotations and reflections: these are easily generated by a simple recursive backtracking search computer program similar to that used for the eight queens puzzle. John Horton Conway and Michael Guy first identified all 240 possible solutions by hand in 1961.