A solid metallic cube having total surface area $ 24 \, \text{m}^2 $ is uniformly heated. If its temperature is increased by $ 10^\circ \, \text{C} $, calculate the increase in volume of the cube.
$ \text{(Given: } \alpha = 5.0 \times 10^{-4} \, \text{C}^{-1} \text{)} $