Answer
$\Rightarrow S_{1}=1$
$\Rightarrow S_{2}=5$
$\Rightarrow S_{3}=14$
$\Rightarrow S_{4}=30$
$\Rightarrow S_{5}=55$
$\Rightarrow S_{6}=91$
Work Step by Step
$S_{n}=\sum ^{n}_{k=1}k^{2}=\dfrac {n\left( n+1\right) \left( 2n+1\right) }{6}$
$\Rightarrow S_{1}=\dfrac {1\times \left( 1+1\right) \left( 2\times 1+1\right) }{6}=1$
$\Rightarrow S_{2}=\dfrac {2\times \left( 2+1\right) \left( 2\times 2+1\right) }{6}=5$
$\Rightarrow S_{3}=\dfrac {3\times \left( 3+1\right) \left( 2\times 3+1\right) }{6}=14$
$\Rightarrow S_{4}=\dfrac {4\times \left( 4+1\right) \left( 2\times 4+1\right) }{6}=30$
$\Rightarrow S_{5}=\dfrac {5\times \left( 5+1\right) \left( 2\times 5+1\right) }{6}=55$
$\Rightarrow S_{6}=\dfrac {6\times \left( 6+1\right) \left( 2\times 6+1\right) }{6}=91$
