To find the number of cube-shaped metal parts produced, we can follow these steps:

1. Calculate the volume of one metal part: The formula for the volume of a cube is:

   $V = a^3$

   where $a$ is the side length of the cube. Here, $a = 6 \, \text{cm}$.

   $V = 6^3 = 216 \, \text{cm}^3$

   Thus, the volume of one metal part is $216 \, \text{cm}^3$.

2. Determine the number of metal parts: The total volume of metal used is $1296 \, \text{cm}^3$. To find the number of metal parts, divide the total volume by the volume of one part:

   $\text{Number of parts} = \frac{\text{Total Volume}}{\text{Volume of One Part}} = \frac{1296}{216}$

   $\text{Number of parts} = 6$

   Therefore, 6 metal parts are produced.

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Final Answer:

The factory produces 6 metal parts.

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Would you like a detailed breakdown of the calculation or have any questions? Here are some related questions for practice:

1. What would be the number of parts produced if the total volume of metal used were 1944 cubic cm?
2. If the side length of the cube is increased to 8 cm, how many parts could be made from 1296 cubic cm?
3. What is the surface area of one metal part with a side length of 6 cm?
4. If one metal part weighs 500 grams, what is the total weight of 6 parts?
5. How would the number of parts change if the side length is reduced to 4 cm?

Tip: Always double-check units to ensure consistent and accurate calculations.