What is the value of $101^{3} - 3 \cdot 101^{2} + 3 \cdot 101 -1$?
I see that this expression has the form $(a - b)^{3} = a^{3} - 3a^{2}b + 3ab^{2} - b^{3}$, where $a = 101$ and $b = 1$. So I can rewrite it as $(101 - 1)^{3}$. Now I just need to evaluate $(100)^{3}$, which is $100 \cdot 100 \cdot 100 = 10^{6}$. Therefore, the value of the expression is $10^{6}$. 