To simplify this expression, we need to first factor the denominators and then combine like terms:

Factor the first denominator:
c^3/c^2-8c+16
= c^3 / (c-4)(c-4)
= c^3 / (c-4)^2

Factor the second denominator:
c^2/c-4
= c^2 / (c-4)

Putting these back into the original expression, we get:

(c^3 / (c-4)^2) - (c^2 / (c-4))

Now, to combine these fractions, we need to find a common denominator. In this case, the common denominator is (c-4)^2, so rewrite the fractions with this common denominator:

(c^3 (c-4) / (c-4)^2) - (c^2 (c-4) / (c-4)^2)

Now that the fractions have a common denominator, we can combine them by subtracting the numerators:

= (c^4 - 4c^3 - c^3 + 4c^2) / (c-4)^2
= (c^4 - 5c^3 + 4c^2) / (c-4)^2

Therefore, the simplified expression is:

(c^4 - 5c^3 + 4c^2) / (c-4)^2