x³+3xy+y³-1
=x³+3x²y+3xy²+y³-3x²y-3xy²+3xy-1
=(x+y)³-1+3xy(1-x-y)
=(x+y-1)[(x+y)²+(x+y)+1]+3xy(1-x-y)
=(x+y-1)(x²-xy+y²+x+y+1)