BALKAN 2014 Problem 2

A special number is a positive integer $n$ for which there exist positive integers $a, b, c$ and $d$ with

$$n=\frac{a^{3}+2 b^{3}}{c^{3}+2 d^{3}}$$

Prove that: (a) there are infinitely many special numbers; (b) 2014 is not a special number.