Solution - Simplification or other simple results

Step  1  :

Trying to factor as a Difference of Cubes:

 1.1      Factoring:  x²⁷-7 

Theory : A difference of two perfect cubes,  a³ - b³ can be factored into
              (a-b) • (a² +ab +b²)

Proof :  (a-b)•(a²+ab+b²) =
            a³+a²b+ab²-ba²-b²a-b³ =
            a³+(a²b-ba²)+(ab²-b²a)-b³ =
            a³+0+0-b³ =
            a³-b³

Check :  7  is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

  x27 - 7