Formula use:

\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3
\left(a-b\right)^3=a^3-3a^2b+3ab^2-b^3
\left(a+b\right)^3=\left(a+b\right)\left(a^2+2ab+b^2\right)
\left(a-b\right)^2=a^2-2ab+b^2

Explanation

Given expression is: 8a^3+{12a}^2+6a-b^3+9b^2-27b+28
Factorize
8a^3+{12a}^2+6a-b^3+9b^2-27b+28
\rightarrow8a^3+12a^2+6a+1-b^3+9b^2-27b+27
\rightarrow\left(2a\right)^3+3.\left(2a\right)^2.1+3.2a.\left(1\right)^2+\left(1\right)^3-\{\left(b\right)^3-3.\left(b\right)^2.3+3.b.\left(3\right)^2-\left(3\right)^3\}
\rightarrow\left(2a+1\right)^3-\left(b-3\right)^3
\rightarrow\left(2a+1-b-3\right)\{\left(2a+1\right)^2+\left(2a+1\right).\left(b-3\right)+\left(b-3\right)^2\}
\rightarrow\left(2a-b-2\right)\left({4a}^2+4a+1+2ab+b-6a-3+b^2-6b+9\right)
\therefore\left(2a-b-2\right)\left(4a^2-2a+7+2ab-5b+b^2\right)
Ans: \left(2a-b-2\right)\left(4a^2-2a+7+2ab-5b+b^2\right)