(a+2b)^2(a^2-2ab+4b^2)^2-(a^2/4+ab+4b^2)(a^2/4-ab+4b^2)(a^2/4-4b^2)

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(a+2b)^2(a^2-2ab+4b^2)^2-(a^2/4+ab+4b^2)(a^2/4-ab+4b^2)(a^2/4-4b^2)
(a+2b)^2(a^2-2ab+4b^2)^2-(a^2/4+ab+4b^2)(a^2/4-ab+4b^2)(a^2/4-4b^2)

(a+2b)^2(a^2-2ab+4b^2)^2-(a^2/4+ab+4b^2)(a^2/4-ab+4b^2)(a^2/4-4b^2)
(a+2b)^2(a^2-2ab+4b^2)^2-(a^2/4+ab+4b^2)(a^2/4-ab+4b^2)(a^2/4-4b^2)
=(a^3+8b^3)^2-(a^2/4+ab+4b^2)(a^2/4-ab+4b^2)(a/2+2b)(a/2-2b)
=(a^3+8b^3)^2-(a^3/8+8b^3)(a^3/8-8b^3)
=a^6+16a^3b^3+64b^6-a^6/64+64b^6
=63a^6/64+16a^3b^3+128b^6

(a+2b)^2(a^2-2ab+4b^2)^2-(a^2/4+ab+4b^2)(a^2/4-ab+4b^2)(a^2/4-4b^2)
=(a^3+8b^3)^2-(a^2/4+ab+4b^2)(a^2/4-ab+4b^2)(a/2+2b)(a/2-2b)
=(a^3+8b^3)^2-(a^3/8+8b^3)(a^3/8-8b^3)
=a^6+16a^3b^3+64b^6-a^6/64+64b^6
=63a^6/64+16a^3b^3+128b^6