Cubic feet is a volume measurement, mostly used for gases rather than liquids (it refers to a volume that is equal to a cube with one foot on each of the three sides). You will see it used for natural gas consumption. It is one way to measure how much fuel was consumed. When you buy natural gas, it is measured in cubic feet; you pay for how many cubic feet you used. the gas is delivered at a fixed (well, ideally constant) pressure which means that volume has a fixed mass. You really are concerned with mass, because mass can be converted into heat content.
That is, the unit "cubic foot" for natural gas has a defined energy content that will get released on burning. So does gasoline, or diesel fuel, or even coal. The things just get measured (and paid for) differently. We use gallons (liquid volume measures) for gasoline and diesel (or heating oil), and weights for solids like coal.
If you compare the volume or unit measurements of consumption, you haven't quite defined the amount of energy involved. That requires a conversion. And even that does not exactly tell you how much energy was produced. It can get a bit complicated when comparing similar energy devices which rely on different fuels, because efficiency is also important (how much of the contained energy in the fuel can be used for heating or moving and how much gets lost to the environment as wasted heat). And the costs for each fuel differ, so even a more efficient furnace that relies on heating oil might be more expensive to use than a less efficient coal furnace or gas furnace, say.
But (in the US) we sell natural gas by the cubic foot (or million cubic ft), gasoline by the gallon (or barrel), and coal by the pound (or ton). Metric equivalents are used in most of the world.