a^8+a^4b^4+b^8
=a^8+2a^4b^4+b^8-a^4b^4
=(a^4+b^4)^2-(a^2b^2)^2
=(a^4+a^2b^2+b^4)(a^4-a^2b^2+b^4)
=(a^4+2a^2b^2+b^4-a^2b^2)(a^4-a^2b^2+b^4)
=[(a^2+b^2)^2-(ab)^2](a^4-a^2b^2+b^4)
=(a^2+ab+b^2)(a^2-ab+b^2)(a^4-a^2b^2+b^4)