1) 3m^3-81=3(m^3-27)=3(m-3)(m^2+3m+9)
2) 4a^2+4ab+4a+b^2+2b=4a(a+b+1)+b(b+2)=(a+b+1)(b+2)(4a+b)
3) b^3-6b^2-6b+1=b^2(b-6)-(6b-1)=(b-6)(6b-1)(b-1)(b+1)
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Answers & Comments
1) 3m^3-81=3(m^3-27)=3(m-3)(m^2+3m+9)
2) 4a^2+4ab+4a+b^2+2b=4a(a+b+1)+b(b+2)=(a+b+1)(b+2)(4a+b)
3) b^3-6b^2-6b+1=b^2(b-6)-(6b-1)=(b-6)(6b-1)(b-1)(b+1)