The length of each side of a cube is doubled, then its volume become………………. Times.

Answer

To find out how many times the volume of a cube increases when the length of each side is doubled, we can follow these steps:

### Step 1: Understand the formula for the volume of a cube.
The volume \( V \) of a cube with side length \( a \) is given by the formula:
\[ V = a^3 \]

### Step 2: Calculate the volume of the original cube.
Let the original side length of the cube be \( a \). Therefore, the volume of the original cube is:
\[ V_{\text{original}} = a^3 \]

### Step 3: Determine the new side length after doubling.
If the length of each side of the cube is doubled, the new side length becomes:
\[ \text{New side length} = 2a \]

### Step 4: Calculate the volume of the new cube.
Using the new side length, the volume of the new cube is:
\[ V_{\text{new}} = (2a)^3 \]

### Step 5: Simplify the expression for the new volume.
Calculating \( (2a)^3 \):
\[ V_{\text{new}} = 2^3 \cdot a^3 = 8a^3 \]

### Step 6: Compare the volumes of the new and original cubes.
Now, we can compare the volume of the new cube to the original cube:
\[ \text{Volume increase factor} = \frac{V_{\text{new}}}{V_{\text{original}}} = \frac{8a^3}{a^3} = 8 \]

### Conclusion:
Thus, when the length of each side of a cube is doubled, its volume becomes **8 times** the original volume.

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