Identify the given information for the cubic polynomial.

Let the zeroes of the cubic polynomial be $\alpha, \beta, \gamma$.
The general form of a cubic polynomial is $P(x) = ax^3 + bx^2 + cx + d$.
The relationships between the zeroes and coefficients are:
Sum of zeroes: $\alpha + \beta + \gamma = -\frac{b}{a}$
Sum of the product of zeroes taken two at a time: $\alpha\beta + \beta\gamma + \gamma\alpha = \frac{c}{a}$
Product of zeroes: $\alpha\beta\gamma = -\frac{d}{a}$

From the problem statement:
Sum of zeroes $= -2$
Sum of the product of its zeroes taken two at a time $= 7$
Product of its zeroes $= 16$

We can assume $a=1$ to find a cubic polynomial.
So, we have:

$$-\frac{b}{1} = -2 \implies b = 2$$ $$\frac{c}{1} = 7 \implies c = 7$$ $$-\frac{d}{1} = 16 \implies d = -16$$

Substitute the values of $a, b, c, d$ into the general form $P(x) = ax^3 + bx^2 + cx + d$.

$$P(x) = 1x^3 + 2x^2 + 7x - 16$$ $$P(x) = x^3 + 2x^2 + 7x - 16$$

The cubic polynomial is $x^3 + 2x^2 + 7x - 16$.