jmc

The given expression is the expansion of $(101-1{)}^3$. In general, the expansion of $(a-b{)}^3$ is equal to $$a^3-3\cdot a^2\cdot b+3\cdot a\cdot b^2-b^3$$

In this case, $a=101,b=1$. Thus $101^3-3\cdot 101^2+3\cdot 101-1=(101-1{)}^3$; we can easily calculate $100^3=\boxed{1000000}$.