# I've been trying and trying... but there does not seem to be three

Consider the expression $$\sqrt {\frac {(n+1)(2n+1)}{6}}$$.

For some whole numbers $$n$$, the expression is also a whole number. Let the three smallest such whole numbers be $$a_{1}, a_{2}, a_{3}$$. Find the value of $$\sum_{i=1}^3 a_{i}$$.

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