A linear unit is used to measure length or distance whereas a cubic unit is used to measure volumes. A cubic unit may defined as a cubic measure (eg a litre) or it could be composed of three linear units (eg cubic centimetre), or a square unit and a linear one (acre-foot). This last combination is rare in the SI system because the linear units are more easily linked to square and cubic units.
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You can't convert that. You can convert linear units to linear units, square units to square units, or cubic units to cubic units.
A rectangle has a perimeter with linear units, and a surface area with square units. It has no cubic units.
Linear units, like inches, can't be converted to cubic units. If they could, then you'd be able to calculate your height in gallons.
No. Just like a length, a perimeter is measured in linear units.
When you say "English", I'm assuming you mean the "customary" system of units of measure that's used in two English speaking countries and a Burmese one. In that system, the volume units of cubic inch, cubic foot, and cubic yard are quite common. Also the cubic mile, though not so commonly heard.