The term NxNxN cube (pronounced "N by N by N cube") or NxNxN puzzle refers to any cubic twisty puzzle which has the same number of cubies in width, length, and height. This generally does not include bandaged cubes unless otherwise mentioned, and this never includes cube-shaped puzzles that don't follow the same general concept as the 2x2x2, 3x3x3, 4x4x4, etc. such as the skewb or the square-1.
Twisty puzzles which fit under this category include the 2x2x2 cube, the Rubik's cube, the 4x4x4 cube, the 5x5x5 cube, and so on. The 1x1x1 Cube also belongs in this category even if it is not a twisty puzzle because it does complete the NxNxN set.