x³-6x²y+12xy²-8y³+1=（x³-8y³）-6xy(x-2y)+1
=(x-2y)(x²+2xy+4y²)-6xy(x-2y)+1
=（x-2y）（x²+2xy+4y²-6xy）+1
=（x-2y）（x²-4xy+4y²）+1
=（x-2y）³+1