Parametric Solutions of the Diophantine Equation $A^2 + nB^4 = C^3$

The Diophantine equation $A^2 + nB^4 = C^3$ has infinitely many integral solutions $A, B, C$ for any fixed integer $n$. The case $n = 0$ is trivial. By using a new polynomial identity we generate these solutions, and then give conditions when the solutions are pairwise co-prime.