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The cube of 7 is 343: 7³ = 7 × 7 × 7 = 343. The small 3 means to use 7 as a factor three times—not to multiply 7 by 3.
How to calculate 7 cubed
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Write the number using exponent notation: 7³.
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Expand the exponent into three factors: 7 × 7 × 7.
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Multiply the first two factors: 7 × 7 = 49.
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Multiply by the remaining factor: 49 × 7 = 343.
Therefore, 7³ = 343. In this expression, 7 is the base and 3 is the exponent. The Papua New Guinea Department of Education explains that multiplying a number by itself three times gives its cube in its Grade 7 lesson on cubes and cube roots.
What does “cubed” mean?
“Seven cubed” and “seven raised to the third power” are two ways to read 7³. The exponent tells you how many times the base appears in the multiplication: three 7s. It does not mean 7 × 3, which equals 21.
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A cube-shaped way to picture 7³
Imagine a cube that is 7 unit blocks long, 7 blocks wide, and 7 blocks high. One layer has 7 × 7 = 49 blocks. Seven such layers contain 49 × 7 = 343 blocks, matching the calculation. This connects cubing a number with the volume of a cube, as described in the University of Waterloo CEMC lesson on exponents. A block model can help make the idea visible, but it is not needed to work out the answer.
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