One cubic metre is 35.3146667215 cubic feet. The number is the linear factor cubed: 1 ÷ 0.3048³, and it is nearly eleven times larger than the area factor of 10.76 for the same pair of length units.
About the units
Both units are derived from their respective length units with no separate definition. What makes the pair worth stating carefully is how fast the factor grows: 3.28 in length, 10.76 in area, 35.31 in volume. Someone who converts a room's dimensions correctly and then guesses at its volume will be wrong by a large margin, and the error always runs the same way — underestimating the metric figure or overestimating the imperial one, depending on direction. The cubic metre is often called a stere in forestry contexts, particularly for firewood, though the term is largely obsolete.
The exact factor
The exact derivation is 1 ÷ 0.3048³ = 1 ÷ 0.028316846592 = 35.3146667214886... The reverse is exact: a cubic foot is 0.028316846592 m³. A useful mental check is that a cubic metre is about 35 cubic feet, so a shipping volume in cubic metres multiplied by 35 gives cubic feet closely enough for a quote. The relationship to the cubic yard is worth adding: 27 cubic feet make a cubic yard, and a cubic yard is 0.7646 m³.
Where you meet this conversion
Freight and shipping, where container capacity, air cargo volume and warehouse space are quoted in cubic metres internationally and cubic feet in American documentation. Construction estimates concrete and excavation in cubic metres or cubic yards depending on country. Timber is traded in cubic metres worldwide, including in the United States for imports, so American mills work in board feet at home and cubic metres for export. Ventilation and air handling rates cross the same boundary as cubic metres per hour against cubic feet per minute.