Continuity of a Piecewise Function

The function $f$ is defined by $f(x) = \begin{cases} k^3 + x & \text{for } x < 3 \\ \displaystyle\frac{16}{k^2 - x} & \text{for } x \geq 3 \end{cases}$, where $k$ is a positive constant. For what value of $k$, if any, is $f$ continuous?