Solution - Simplification or other simple results

Step  1  :

Trying to factor as a Difference of Cubes:

 1.1      Factoring:  t³-216 

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 :  t³ is the cube of   t¹

Factorization is :
             (t - 6)  •  (t² + 6t + 36) 

Trying to factor by splitting the middle term

 1.2     Factoring  t² + 6t + 36 

The first term is,  t²  its coefficient is  1 .
The middle term is,  +6t  its coefficient is  6 .
The last term, "the constant", is  +36 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 36 = 36 

Step-2 : Find two factors of  36  whose sum equals the coefficient of the middle term, which is   6 .

For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  (t - 6) • (t2 + 6t + 36)