square pyramidal numbers proof    proof outline  It is possible to write down this formula  This is an alternative way to group the sum of the squares to quote an example we assume n       In this representation the number five is summed  times the number  is summed  times and so on until zero After that it is possible to use this result to solve the summation  The main formula is equivalent to  After some agebraic manipulation it is possible to obtain  This is equivalent to the desired formula