Answer :

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trying to factor as a Difference of Cubes:

 1.1      Factoring:  x3-216 

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:  216  is the cube of   6 
Check:  x3 is the cube of   x1

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