Mathematical Induction>

There is a difficult MI question that bothering me for 3 months. it is difficult to understand.
Here it is:

Prove,by mathematical induction,that for all positive integers n, the following proposition is true.

n*1+(n-1)*2+(n-2)*3+...+3*(n-2)+2*(n-1)+1*n=1/6 n(n+1)(n+2)

p.s. *=times
I am going to have the examination soon. Please answer my quesion as soon as possible.
Thank you very much! ><
Thx!