is (x^8 - 6561) a perfect square?

I think you may mean " a difference of two squares"

(x^8 - 6561) =

(x^8 - 3^8)  =

( x^4 - 3^4) ( x^4 + 3^4)  =

[ (x^2)^2  - (3^2)^2 ]  [ (x^2)^2 + (3^2)^2 ]

So....it is a difference of  two squares

thank you

thank you