16.97cm

\begin{align}
&\text{Let the diagonal be}\ d\\
&d\ \text{is the hypotenuse}\\
&\text{with sides of cubes as other two sides}\\
&\begin{aligned}
d^{2}&=12^{2}+12^{2} \\
d^{2}&=144+144 \\
d^{2}&=288 \\
d&=\sqrt{288} \\
d&=16.970 \ldots \\
d &\approx 16.97 \mathrm{~cm}
\end{aligned}\end{align}