Can a number of the form $n = {2^r}{b^2}$ always be represented as a sum of two squares, if $r \geq 1$ and $b$ is an odd composite?

Question

Can a number of the form $n = {2^r}{b^2}$ always be represented as a sum of two squares, if $r \geq 1$ and $b$ is an odd composite?

More generally:

Can a number of the form $n = {2^r}{b^2}$ always be represented as a sum of two squares, if $r \geq 1$?

Answer 1

Yes, because $$2^{2m+1}b^2=(2^mb)^2+(2^mb)^2$$ and $$2^{2m}b^2=0^2+(2^mb)^2$$