Question:
\[ \frac{ (a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3 }{ (a-b)^3+(b-c)^3+(c-a)^3 } \]
Solution:
\[ = \frac{ [(a-b)(a+b)]^3+[(b-c)(b+c)]^3+[(c-a)(c+a)]^3 }{ (a-b)^3+(b-c)^3+(c-a)^3 } \]
\[ = \frac{ (a-b)^3(a+b)^3+(b-c)^3(b+c)^3+(c-a)^3(c+a)^3 }{ (a-b)^3+(b-c)^3+(c-a)^3 } \]
\[ = \frac{ 3(a-b)(a+b)(b-c)(b+c)(c-a)(c+a) }{ 3(a-b)(b-c)(c-a) } \]
\[ = (a+b)(b+c)(c+a) \]
\[ \boxed{(a+b)(b+c)(c+a)} \]