Verified answer

a³ - b³ = (a - b)(a² + ab + b²)

a³ + b³ = (a + b)(a² - ab + b²)

-----

1/8 - a³ = (1/2)³ - a³ = (1/2 - a)(1/4 + a/2 + a²)

1/27*x³ - 1 = (x/3)³ - 1³ = (x/3 - 1)(x²/9 + x/3 + 1)

1/8c³ + 1 = (c/2)³ + 1³ = (c/2 + 1)(c²/4 - c/2 + 1)