You can simply calculate "equivalent" cross-sectional stiffness values.
Note that all non-zero terms of the stiffness matrix depend on one of these values: $EA$ or $EI$. These are the cross-sectional axial and rotational stiffnesses, respectively.
Obviously, when looking at entire beams, another important parameter is the beam's length $L$ (to multiple exponents), but here we're just looking at the cross-section, so we only care about $EA$ and $EI$.
Given that the stiffness matrix only cares about $EA$ and $EI$, we can actually replace them entirely with $K_a$ and $K_r$ (axial and rotational stiffness).
The wonderful thing about doing this is that it exposes an important aspect of the stiffness matrix: it doesn't care about the beam's elastic modulus, area or moment of inertia. It only cares about its stiffness.
We can therefore do whatever we want with $E$, $A$ and $I$ as we see fit, so long as we get a reasonable stiffness at the end.
In this case, we're dealing with a composite beam made up of a square concrete section and a hollow square steel section. How do we find the stiffness of this beam? Well, a good first guess is to simply add the stiffness of each of component:
$$\begin{align}
K_a &= E_c A_c + E_s A_s \\
K_r &= E_c I_c + E_s I_s
\end{align}$$
(the math is a bit simple in this case since both concrete and steel have the same centroid; if that weren't the case, then their moments of inertia would have to be calculated relative to the composite centroid, see here an example of how to do so)
This is a pretty conservative method: you aren't taking into consideration any interaction between the components. For example, the concrete's true axial stiffness will likely be larger than $E_c A_c$ due to the lateral constraint imposed by the steel section (as described here).
