For example, I have:

$a=\sum _{r=1}^n x_r
   \left(\left(\sum _{i=1}^n
   x_i-x_r\right){}^2-\sum
   _{i=1}^n x_i^2\right)$

`a = \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(r = 1\), \(n\)]\((
\*SubscriptBox[\(x\), \(r\)] \((\((
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(n\)]
\*SubscriptBox[\(x\), \(i\)] - 
\*SubscriptBox[\(x\), \(r\)])\)^2 - 
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(n\)]\((
\*SubscriptBox[\(x\), \(i\)]^2)\))\))\)\)`

and $\sum _{i=1}^n x_i=s_1, \sum _{i=1}^n x_i^2=s_2, \sum _{i=1}^n x_i^3=s_3$

`\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(n\)]
\*SubsuperscriptBox[\(x\), \(i\), \(2\)]\) == s2`

I would like to represent $a$ by $s_1, s_2, s_3$, how should I do it? I tried Solve or Eliminate, but couldn't find a way.