If a = ( √2 -1)1/3, then the value of (a - a-1)3 + 3 ( a - a -1 ) is?

Given that,
a = (√2 - 1)^1/3
By cubing the both side of the given equation.
a³ = √2 - 1
Then 1/a³ = 1/√2 - 1
Now multiply and divide the above equation by √2 + 1
⇒ 1/a³ = ( √2 + 1 ) / ( √2 + 1 ) x 1/(√2 - 1 )
⇒ 1/a³ = ( √2 + 1 ) x 1 / ( √2 + 1 ) x (√2 - 1 ) [ Use the formula (A + B)(A - B) = A² - B² ]
⇒ 1/a³ = ( √2 + 1 ) / ( 2 - 1 )
⇒ 1/a³ = √2 + 1
According to the question
( a - a^-1 )³ + 3 ( a - a^-1 )
= (a - 1/a)³ + 3(a - 1/a) Use the formula [ ( A - B)³ = A³ - B³ + 3AB(A - B) ]
= a³ - 1/a³ - 3 a x 1/a (a -1/a) + 3(a - 1/a)
= a³ - 1/a³ - 3 (a -1/a) + 3(a - 1/a)
= a³ - 1/a³
Pu the value of a³ and 1/a³
= √2 -1 - ( √2 + 1 )
= √2 -1 - √2 - 1
= -2