The cubic foot is a unit of volume in the imperial unit system with the symbol ft³.
1 cubic foot is equal to 1/27 yd³ or 1728 in³. It is equal to the volume of a cube measuring 1ft on each side.
One cubic foot of water weighs 62.4 lbs or 28.29 kg.
The barrel is a unit of volume used in the oil industry with the symbol bbl.
Oil is more commonly expressed in terms of cubic metres (m³) but in the US and in the economic world (mainly because such a large percentage of the world's oil is shipped to the US) as barrels.
The measurement of the barrel originated in the US at the first oil well in Pennsylvania. There were so many variants of barrel size (including those used for wine and other goods) that the distrust became so prevalent a central and standard barrel size was created. This was finally established in 1872 as 42 US gallons.