Divisibility of Exponential Difference

For $n = 1$, $7^6 - 6^6 = (7^3 - 6^3)(7^3 + 6^3) = (343 - 216)(343 + 216) = 127 \times 559$. Also, $559 = 13 \times 43$. Thus, $7^{6n} - 6^{6n}$ is divisible by $13$, $127$, and $559$. Hence, 'All of these' is the correct answer.