2017/012) Can $5^{64}-3^{64}$ be expressed as sum of 2 squares

we have $5^{64}-3^{64}= (5^{32} + 3^{32})(5^{32} - 3^{32})$
$= (5^{32} + 3^{32})(5^{16} + 3^{16})(5^{16} - 3^{16})$
$= (5^{32} + 3^{32})(5^{16} + 3^{16})(5^{8} + 3^{8})(5^{4} + 3^{4})(5^{4} - 3^{4})$
$= (5^{32} + 3^{32})(5^{16} + 3^{16})(5^{8} + 3^{8})(5^{4} + 3^{4})(5^{2} + 3^{2})(5^{2} - 3^{2})$
$= (5^{32} + 3^{32})(5^{16} + 3^{16})(5^{8} + 3^{8})(5^{4} + 3^{4})(5^{2} + 3^{2}) * 16$
the above is product of sum of squares( knowing that $16= 4^2 +0^2$ the above can be expressed as sum of squares