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.