7 6n - 6 6n, where n is an integer greater than 0, is divisible by

For n =1
7⁶ⁿ - 6⁶ⁿ = 7⁶ - 6⁶
⇒ ( 7³ )² - ( 6³ )²
⇒ ( 7³ - 6³ )( 7³ + 6³ )
= ( 343 - 216 )( 343 + 216 )
= 127 x 559
∴ it is clearly divisible by 127.