If and let us calculate the followings :

a + b =

a + b = = = = 3

a-b =

a-b = = = = √5

ab = = 1

(a + b)³ = a³ + b³ + 3ab(a + b)

a³ + b³ = (a + b)³ - 3ab(a + b)

= (3)³ – 3 × 1 × 3

= 27 – 9 = 18

(a-b)³ = a³-b³-3ab(a-b)

a³-b³ = (a-b)³ + 3ab(a-b)

= (√5)³ + 3 × 1 × (√5)

= 5√5 + 3√5

= √5 [5 + 3]

= 8√5