Let the third power of polynomial X - the second power of 6x y + the second power of 12xy - the third power of 8y + 1 be written as the sum of two integers, so that one of them does not contain letters

Let the third power of polynomial X - the second power of 6x y + the second power of 12xy - the third power of 8y + 1 be written as the sum of two integers, so that one of them does not contain letters

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