To simplify the given expression, we can start by factoring the numerator and the denominator.

The numerator can be factored using the difference of cubes formula:

m^6 - 16m^3 + 64 = (m^2)^3 - 4^2(m^3) + 4^3 = (m^2 - 4)^3

The denominator can be factored using basic algebraic methods:

m^2 + 2m + 4 = (m + 2)^2
m^3 - 8 = (m - 2)(m^2 + 2m + 4) = (m - 2)(m + 2)^2

Now, substitute the factored forms into the expression:

S = [(m^2 - 4)^3]/[(m + 2)^2(m - 2)(m + 2)^2]

Next, simplify the expression:

S = (m^2 - 4)^3 / [(m + 2)(m - 2)(m + 2)^3]

Therefore, the simplified form of the expression is S = (m^2 - 4)^3 / [(m + 2)(m - 2)(m + 2)^3]