One cubic inch is exactly 16.387064 millilitres. Every digit is definitional, since the inch is exactly 2.54 cm and 2.54³ = 16.387064 — one of the rare cubed conversions that terminates.
About the units
The cubic inch is the small-volume unit of the imperial and US customary systems, and it has one job in modern use that keeps it alive: engine displacement. American engines have historically been described in cubic inches, and the tradition survives in muscle car culture and in aviation piston engines. Elsewhere displacement is given in litres or cubic centimetres, and a cubic centimetre is exactly a millilitre. The cubic inch is also the unit through which the US gallon is defined, at exactly 231 in³, so it sits at the root of the entire American liquid measure system.
The exact factor
The derivation is 2.54³ = 16.387064 exactly, so 1 in³ = 16.387064 ml = 16.387064 cm³. The conversions that matter in practice are engine sizes: a 350 cubic inch V8 is 5,735 cm³, quoted as 5.7 litres; a 302 is 4,949 cm³ or 5.0 litres; and a 427 is 6,997 cm³, the famous 7.0-litre. Going the other way, a 2.0-litre engine is 122 cubic inches. The rounding in marketing names is generous in both directions.
Where you meet this conversion
Engine displacement, both automotive and aviation. American piston aircraft engines are described in cubic inches — the Lycoming O-360 is 360 in³, 5.9 litres — and their manuals mix that with metric fluid capacities. Compressor and pump displacement, hydraulic cylinder volumes and some packaging specifications use it. Because the US gallon is defined as 231 cubic inches, any exact conversion of American liquid measures ultimately passes through this number.