Give all possible rational zeros for the following polynomial function.
\[
f(x)=3 x^{3}+65 x^{2}+65 x+27
\]

Step 1 ：The Rational Root Theorem states that the possible rational roots of a polynomial equation are given by the factors of the constant term divided by the factors of the leading coefficient.

Step 2 ：In this case, the constant term is 27 and the leading coefficient is 3.

Step 3 ：We need to find all the factors of 27 and 3.

Step 4 ：The factors of 27 are \(1, 3, 9, 27\).

Step 5 ：The factors of 3 are \(1, 3\).

Step 6 ：We then divide each factor of 27 by each factor of 3 to get all possible rational roots.

Step 7 ：The possible rational roots are \(\pm \frac{1}{3}, \pm 1, \pm 3, \pm 9, \pm 27\).

Step 8 ：Final Answer: The possible rational zeros for the polynomial function are \(\boxed{\pm \frac{1}{3}, \pm 1, \pm 3, \pm 9, \pm 27}\).