A³+27b³=(a+3b)(a²-3b+9b²)
(a-b)³+b³=(a-b+b)((a-b)²-(a-b)b+b²)=a(a²-2ab+b²-ab+b²+b²)=a(a²-3ab+3b²)
m³n³-k³=(mn-k)(m²n²+mnk+k²)
(x-2)³-27=(x-2-3)((x-2)²+3(x-2)+9)=(x-5)(x²-4x+4+3x-6+9)=(x-5)(x²-x+7)
8a³+(a-b)³=(2a+a-b)(4a²-2a(a-b)+(a-b)²)=(3a-b)(4a²-2a²+2ab+a²-2ab+b²)=(3a-b)(3a²+b²)
27x³-y³(x-y)³=(3x-y(x-y))(9x²+3xy(x-y)+y²(x-y)²)=(3x-xy+y²)(9x²+3x²y-3xy²+x²y²-2xy³+y^4)