A hardly known factorization

If you get the command to factorize a4 + b4 most people with a little sense of mathematics tell you
that it cannot be done because the sum of two squares cannot be factorized and
a4 and b4 are a square each for sure.
a4 = (a2)2, so a square.

It really can be factorized. Look.

a4 + b4 =
a4 + 2(ab)2 + b4 - 2(ab)2 =
(a2 + b2)2 - (ab√2)2 =
(a2 - ab√2 + b2)(a2 + ab√2 + b2)

On this site is not discussed, whether the found two factors can be factorized.

Higher exponents of a and b

As well is right: a4n + b4n = (a2n - (ab)n √2 + b2n)(a2n + (ab)n √2 + b2n)
The n is a natural number.

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