A Geometrical Way to Sum Powers by Means of Tetrahedrons and Eulerian   Numbers
  We geometrically prove that in a d-dimensional cube with edges of length n, the number of particular d-dimensional tetrahedrons are given by Eulerian numbers. These tetrahedrons tassellate the cube, In this way the sum of the cubes are the sums of the tetrahedrons, whose calculation is trivial. 
Mario Barra
math.HO