Answer
$58$
Work Step by Step
$\sum ^{6}_{i=1}\left( 2+i-i\right) ^{2}=\sum ^{6}_{i=1}2+\sum ^{6}_{i=1}i-\sum ^{6}_{i=1}i^{2}=2\times n+\dfrac {n\left( n+1\right) }{2}-\dfrac {n\left( n+1\right) \left( 2n+1\right) }{6}=2\times 6+\dfrac {6\times \left( 6+1\right) }{2}-\dfrac {6\times \left( 6+1\right) \left( 2\times 6+1\right) }{6}=58 $