jmc

First let's compute the volume of the container. The container measures $10\times 10\times 10$ so its volume is $$10\cdot 10\cdot 10=10^3=1000$$inches cubed. Since the container is only half full, there are $$\frac{1}{2}\cdot 10^3=500$$inches cubed of water in it. Additionally, there are ten ice cubes each with a volume of $2^3$. This means that the total volume of the ice cubes is $$10\cdot 2^3=10\cdot 8=80.$$Altogether, the water and the ice cubes occupy $500+80=580$ inches cubed. This means that there are $1000-580=\boxed{420}$ inches cubed of space in the container unoccupied by water and ice.