Let $ n$ be a natural number. A cube of edge $ n$ may be divided in 1996 cubes whose edges length are also natural numbers. Find the minimum possible value for $ n$.
1. **Establishing the minimum value of \( n \):**
   - We need to divide a cube of edge length \( n \) into 1996 smaller cubes, each with natural number edge lengths.
   - The maximum number of smaller cubes we can obtain from a cube of edge length \( n \) is \( n^3 \).
   - Therefore, we need \( n^3 \geq 1996 \).

2. **Finding the smallest \( n \) such that \( n^3 \geq 1996 \):**
   - Calculate the cube root of 1996:
     \[
     \sqrt[3]{1996} \approx 12.6
     \]
   - Since \( n \) must be a natural number, we round up to the nearest whole number:
     \[
     n = 13
     \]
   - Verify:
     \[
     13^3 = 2197
     \]
     Since \( 2197 \geq 1996 \), \( n = 13 \) is a valid candidate.

3. **Dividing the cube of edge length 13 into 1996 smaller cubes:**
   - A cube of edge length 13 can be divided into \( 13^3 = 2197 \) unit cubes (each of edge length 1).
   - We need exactly 1996 cubes, so we have an excess of:
     \[
     2197 - 1996 = 201 \text{ unit cubes}
     \]

4. **Adjusting the number of cubes:**
   - To reduce the number of unit cubes, we can combine some of them into larger cubes.
   - Combine 8 unit cubes to form one cube of edge length 2:
     \[
     8 \text{ unit cubes} \rightarrow 1 \text{ cube of edge length 2}
     \]
   - We need to reduce the number of unit cubes by 201, so we can form:
     \[
     \left\lfloor \frac{201}{7} \right\rfloor = 28 \text{ cubes of edge length 2}
     \]
     (since each cube of edge length 2 replaces 7 unit cubes, we need 28 such cubes to replace 196 unit cubes)
   - This leaves us with:
     \[
     201 - 196 = 5 \text{ unit cubes}
     \]

5. **Final adjustment:**
   - We now have 28 cubes of edge length 2 and 5 unit cubes.
   - Total number of cubes:
     \[
     28 + 5 = 33 \text{ cubes}
     \]
   - We need 1996 cubes, so we need to form additional 1963 cubes of edge length 1.

6. **Conclusion:**
   - The minimum value of \( n \) that allows us to divide a cube into exactly 1996 smaller cubes, each with natural number edge lengths, is \( n = 13 \).

The final answer is \( \boxed{ n = 13 } \)