NO, you would not. Anything like that is commonly measured as an AREA
Cubic inches is probably most likely, although gallons is also possible.
You would answer it with cubic feet
cubic feet if a cube and square feet if a square shape
cubic metres
Cubic kilometres.
You are free to measure the pool with any units of volume that you like, it doesn't have to be cubic feet.
Anything cubed. Examples: cubic feet, cubic inches, cubic yards, cubic centimeters, cubic meters, cubic miles, cubic kilometers...
Cubic yards.
1000 cubic centimeters is a measure of volume; the only "exact equivalant in volume" possible would be in another measure of volume, such as cubic inches, cubic feet, cubic meters, etc.
Probably cubic inches. Gallons would be possible.
Litres. I would use either cubic centimeters or cubic inches.
Cubic metres, or cubic kilometres for large lakes.