Value of summation $ij$ What is the value of $\sum \limits_{1 \le i < j \le 10} ij$?

$$\sum_{1\le r\le n}r\left(\sum_{r+1\le s\le n}s\right)$$
$$=\sum_{1\le r\le n}r\{\sum_{1\le s\le n}s-\sum_{1\le s\le r}s\}$$
$$=\sum_{1\le r\le n}r\{\frac{n(n+1)}2-\frac{r(r+1)}2\}$$
$$=\frac{n(n+1)}2\sum_{1\le r\le n}r- \frac12\{\sum_{1\le r\le n}r^3+\sum_{1\le r\le n}r^2\}$$
Now, you know 
$\sum_{1\le r\le n}r=\frac{n(n+1)}2,$
$\sum_{1\le r\le n}r^2=\frac{n(n+1)(2n+1)}6,$
$\sum_{1\le r\le n}r^3=\left(\frac{n(n+1)}2\right)^2$
