Formula use:
a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)
Explanation
Given expression is: a^3b^3c^3-1
Factorize
a^3b^3c^3-1
\rightarrow\left(abc\right)^3-\left(1\right)^3
\rightarrow\left(abc-1\right)\{\left(abc\right)^2+abc.1+\left(1\right)^2\}
\therefore\left(abc-1\right)\left(a^2b^2c^2+abc+1\right)
Ans: \left(abc-1\right)\left(a^2b^2c^2+abc+1\right)