A number theory problem by stephen liado

By Euler's Theorem $7^6 \equiv 1 \pmod{9}$

Thus, $2014^{2015} \equiv 7^{2015} \equiv 7^5 \equiv (-2)^{5} \equiv -32 \equiv 4 \pmod{9}$

Hence, the answer is $\boxed{4}$