Find All The Equations !

Given $216$ equations that we can form from $x^{12}+ ax^8+ bx^4+ c=y^6$ where $a , b , c$ positive integers which satisfy $3 \leq a \leq 5 , 4 \leq b \leq 12$ , and $1 \leq c \leq 8$ . Let $n$ donate the number of those equations which are solvable in positive integers . Then, what is the value of $n^{10^{2014}}$ mod $2014$ ?