1) a³ - 27b³ = (a - 3b)(a² + 3ab + 9b²)

2) m³n³ + k³ = (mn)³ + k³ = (mn + k)((mn)² - mnk + k²) = (mn + k)(m²n² - kmn + k²)

3) x⁶ - y⁶ = (x³ - y³)(x³ + y³) = (x - y)(x + y)(x² + xy + y²)(x² - xy + y²)

4) k⁶ + (pq)⁶ = (k²)³ + (p²q²)³ = (k² + p²q²)((k²)² - k²p²q² + (p²q²)²) = (k² + p²q²)(k⁴ - k²p²q² + p⁴q⁴)

5) (a - b)³ + b³ =  (a - b + b)(a² - 2ab + b² - ab + b² + b²) = a(a² - 3ab + 3b²)

6) (x - 2)³ - 27 = (x - 2 - 3)(x² - 4x + 4 + 3x - 6 + 9) = (x - 5)(x² - x + 7)

7) 8a³ + (a - b)³ = (2a + a - b)(4a² - 2a² + 2ab + a² - 2ab + b²) = (3a - b)(3a² + b²)

8) 27x³ - y³(x - y)³ = (3x - y(x - y))(9x² + 3x²y - 3xy² + (xy - y²)²) = (3x - xy + y²)(9x² + 3x²y - 3xy² + x²y² - 2xy³ + y⁴)