factorize ` 1 + b^3 + 8c^3 - 6bc`

Explanation

`1+b^3+8c^3-6bc`

`=(1)^3+b^3+(2c)^3 -3(1)(b)(2c)`

Using `a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)`

`(1)^3+b^3+(2c)^3 -3(1)(b)(2c)=(1+b+2c)(1+b^2+4c^2-b-2bc-2c)`, which are the required factors.