The factors of 8a3+b3−6ab+1 are:
(2a+b−1)(4a2+b2+1−3ab−2a)
(2a−b+1)(4a2+b2−4ab+1−2a+b)
(2a+b+1)(4a2+b2+1−2ab−b−2a)
(2a−1+b)(4a2+1−4a−b−2ab)
(2a)3+(b)3+(1)3−3×2a×b×1=(2a+ab+1)[(2a)2+b2+1−2a×b−b×1−1×2a]=(2a+ab+1)(4a2+b2+1−2ab−b−2a)