One cubic foot is exactly 28.316846592 litres. The value follows from the foot being exactly 0.3048 metres: cube that and you get 0.028316846592 cubic metres, which is the same number of litres.
About the units
The cubic foot is the imperial and US customary unit for volumes larger than a gallon, and it is the standard measure for gas, storage space and bulk materials in American practice. The litre is one cubic decimetre. The two sit at similar scales — a cubic foot is a bit over 28 litres — which makes them natural competitors for the same jobs. The cubing is the thing to watch: a foot is 3.28 times shorter than a metre in the sense that 3.28 feet make a metre, but a cubic metre holds 35.3 cubic feet, because the factor cubes.
The exact factor
The derivation is 0.3048³ = 0.028316846592 m³, and since one cubic metre is a thousand litres, that is 28.316846592 litres. Both directions are exact. Related values worth having: a cubic foot is 7.48 US gallons and 6.23 imperial gallons, and 35.3147 cubic feet make a cubic metre. The gas industry uses the standard cubic foot, which specifies a temperature and pressure as well as a volume, and that is a different quantity again — comparing it to a plain cubic foot without the conditions is meaningless.
Where you meet this conversion
Natural gas billing in the United States is per hundred or per thousand cubic feet while European bills are in cubic metres or kilowatt-hours. Refrigerator and freezer capacity is quoted in cubic feet in American listings and litres in European ones, so the same appliance is a 20 cu ft model or a 566 litre model. Air compressors, ventilation rates and shipping container volumes all use one unit inside the United States and the other internationally.