What is the law of calculating 2 * 22 * 22 222 * 222 2222 * 2222?

What is the law of calculating 2 * 22 * 22 222 * 222 2222 * 2222?

=2^2
=22^2
=222^2
...
=4*1^2
=4*11^2
=4*111^2
...
=4*(10^n+10^(n-1)+...+10+1)^2
=4*(1*(1-10^n)/(1-10))^2
=(4/81)*(10^n-1)^2