Why are the sum of squares afraid of one cube?

Calculus Level 2

limn12+22+32+...+n2n3\lim _{ n\rightarrow \infty }{ \frac { { 1 }^{ 2 }+2^{ 2 }+3^{ 2 }+...+n^{ 2 } }{ { n }^{ 3 } } } can be expressed in the form ab\frac { a }{ b } . Find a+ba+b

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