It isn't clear what sorts of units you are talking about.
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cubic feet is a unit of volume and a mile per hour is a unit of speed. The two are not compatible, the question is nonsensical.
A cubic foot is a unit of volume. An inch is a unit of distance. The two units are therefore incompatible.
Cubic feet is one unit of measurement of volume, though any cubic unit of measurement (cubic centimeters, cubic yards, ect.) is representative of a volume.
A linear foot is a unit of length. A cubic inch is a unit of volume. The two units are therefore incompatible.
You can't do that, because "cubic feet" and "miles" don't convert to each other. The first is a unit of volume, and the second is a unit of length or distance. There's no way to figure how many yards of gas you put in your gas-tank, or how many cubic feet it is from your house to your job.