\[\large \frac{1^2+2^2+3^2+\cdots+2012^2+2013^2+2014^2}{1+2+3+\cdots+2012+2013+2014} = \ ? \]

**Hint**: \( 1^2 + 2^2 + 3^2 + \cdots + n^2= \frac16 n(n+1)(2n+1) \).

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