Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "a1"   was replaced by   "a^1". 

Step  1  :

Trying to factor as a Difference of Cubes:

 1.1      Factoring:  q³-a 

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 :  q³ is the cube of   q¹

Check :  a ¹ is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

  q3 - a