Find the values of the following by using suitable identity:
`(396)^(3)`

Answer

To find the value of \( (396)^3 \) using a suitable algebraic identity, we can express 396 as \( 400 - 4 \). This allows us to use the identity for the cube of a binomial, which is:

\[ (a - b)^3 = a^3 - b^3 - 3ab(a - b) \]

### Step-by-Step Solution:

1. **Identify \( a \) and \( b \)**:
- Let \( a = 400 \) and \( b = 4 \).
- Thus, we want to calculate \( (400 - 4)^3 \).

2. **Apply the identity**:
- Using the identity \( (a - b)^3 = a^3 - b^3 - 3ab(a - b) \), we substitute \( a \) and \( b \):
\[ (400 - 4)^3 = 400^3 - 4^3 - 3 \cdot 400 \cdot 4 \cdot (400 - 4) \]

3. **Calculate \( a^3 \) and \( b^3 \)**:
- Calculate \( 400^3 \):
\[ 400^3 = 64000000 \]
- Calculate \( 4^3 \):
\[ 4^3 = 64 \]

4. **Calculate \( 3ab(a - b) \)**:
- First, calculate \( 3 \cdot 400 \cdot 4 \):
\[ 3 \cdot 400 \cdot 4 = 4800 \]
- Then calculate \( (400 - 4) \):
\[ 400 - 4 = 396 \]
- Now multiply:
\[ 4800 \cdot 396 = 1900800 \]

5. **Combine all parts**:
- Substitute back into the equation:
\[ (400 - 4)^3 = 64000000 - 64 - 1900800 \]
- Calculate:
\[ 64000000 - 64 = 63999936 \]
- Now subtract \( 1900800 \):
\[ 63999936 - 1900800 = 62099136 \]

6. **Final Answer**:
- Therefore, \( (396)^3 = 62099136 \).

### Summary:
The value of \( (396)^3 \) is \( 62099136 \).