BALKAN-SL 2014 N4

A special number is a positive integer $n$ for which there exists positive integers $a$, $b$, $c$, and $d$ with $$n = \frac {a^3 + 2b^3} {c^3 + 2d^3}.$$ Prove that

i) there are infinitely many special numbers; ii) $2014$ is not a special number.

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