Find the Sum $\sum _ { k = 1 } ^ { n } \left( k ^ { 3 } + k ^ { 2 } \right)$

Find the sum.
- $\sum _ { k = 1 } ^ { n } \left( k ^ { 3 } + k ^ { 2 } \right)$

A) $\frac { n ( 2 n + 1 ) ^ { 2 } } { 4 } + \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 }$
B) $\frac { \mathrm { n } ( \mathrm { n } + 1 ) ^ { 2 } } { 4 } + \frac { \mathrm { n } ( \mathrm { n } + 1 ) ( 2 \mathrm { n } + 1 ) } { 6 }$
C) $\frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } + \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 }$
D) $\frac { n ^ { 3 } ( n + 1 ) ^ { 2 } } { 4 } + \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 }$

Correct Answer:

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