To find \(f(x)\), we need to integrate \(f'(x) = 6x^2 - \frac{8}{x^2}\).

Integrate term by term:

\(\int 6x^2 \, dx = 2x^3 + C_1\)

\(\int -\frac{8}{x^2} \, dx = 8x^{-1} + C_2\)

Thus, \(f(x) = 2x^3 + \frac{8}{x} + C\).

Given that the curve passes through \((2, 7)\), substitute \(x = 2\) and \(f(x) = 7\):

\(7 = 2(2)^3 + \frac{8}{2} + C\)

\(7 = 16 + 4 + C\)

\(7 = 20 + C\)

\(C = -13\)

Therefore, \(f(x) = 2x^3 + \frac{8}{x} - 13\).