Answer
$6\times \left( 6+3\right) +7\times \left( 7+3\right) +8\times \left( 8+3\right) +9\times \left( 9+3\right) =54+70+88+108=320$
Work Step by Step
$\sum ^{9}_{k=6}k\left( k+3\right) =6\times \left( 6+3\right) +7\times \left( 7+3\right) +8\times \left( 8+3\right) +9\times \left( 9+3\right) =54+70+88+108=320$
