(a^2 - b^2)^3:
(a^2 - b^2)^3 = (a^2 - b^2)(a^2 - b^2)(a^2 - b^2)
Expand using the formula for the difference of squares (a^2 - b^2 = (a + b)(a - b)):
(a + b)(a - b)(a + b)(a - b)(a + b)(a - b)
= (a^2 - b^2)(a^2 - b^2)(a^2 - b^2)
= (a^4 - 2a^2b^2 + b^4)(a^2 - b^2)
= a^6 - 2a^4b^2 + a^2b^4 - a^4b^2 + 2a^2b^4 - b^6
= a^6 - 3a^4b^2 + 3a^2b^4 - b^6

(m^2 + n^2)^3:
(m^2 + n^2)^3 = (m^2 + n^2)(m^2 + n^2)(m^2 + n^2)
Expand using the formula for the sum of squares (m^2 + n^2 = (m + n)^2 - 2mn):
(m + n)^2 - 2mn)(m + n)^2 - 2mn)(m + n)^2 - 2mn
= (m^2 + 2mn + n^2 - 2mn)(m^2 + 2mn + n^2 - 2mn)(m^2 + 2mn + n^2 - 2mn)
= (m^4 + 2m^3n + m^2n^2 - 2m^3n - 4m^2n^2 - 2mn^3 + m^2n^2 + 2mn^3 + n^4 - 2m^2n^2 - 4mn^3 - 2n^4)
= m^6 + 3m^4n^2 + 3m^2n^4 + n^6

(2a^2 + b^2)^3:
(2a^2 + b^2)^3 = (2a^2 + b^2)(2a^2 + b^2)(2a^2 + b^2)
Expand using the formula for the sum of squares ((2a)^2 + b^2 = (2a + b)(2a - b)):
(2a + b)(2a - b)(2a + b)(2a - b)(2a + b)(2a - b)
= (4a^2 - b^2)(4a^2 - b^2)(4a^2 - b^2)
= (16a^4 - 2b^2)(16a^4 - b^2)
= 256a^8 - 32a^4b^2 - 16a^4b^2 + 2b^4
= 256a^8 - 48a^4b^2 + 2b^4