Answer:
See explanation below
Step-by-step explanation:
Case 1) x is even ⇒ x³ is even
x = 2k for some k
⇒x³ = (2k)³= 8k³ = 2(4k³) which is even.
Case 2) x is odd⇒x³ is odd
x = 2k - 1 for some k
⇒x³ = (2k - 1)³ = (2k)³- 3(2k)²(1) + 3(2k)(1)² -(1)³ = 8k³- 12k² + 6 - 1 = 2 (4k³ - 6k² + 3) - 1 which is odd.
