To solve this problem, we are given the volume of a cube, $V = 2070 \, \text{cm}^3$, and asked to find the length of each side, denoted as $s$, accurate to two decimal places.

The formula for the volume of a cube is: $V = s^3$ To find $s$, we take the cube root of the volume: [ s = \sqrt[3]{V} = \sqrt[3]{2070} ]

Let's compute this: $s \approx \sqrt[3]{2070} \approx 12.74 \, \text{cm}$

So, the length of each side of the cube is approximately 12.74 cm, which matches the first option in the provided choices.

The correct answer is: $\boxed{12.74 \, \text{cm}}$

Would you like more details or have any further questions?

Here are 5 related questions you might want to explore:

1. How do you calculate the volume of a rectangular prism?
2. What is the formula for the surface area of a cube?
3. How does the volume of a cube change if you double the side length?
4. What is the relation between the volume and surface area of a cube?
5. How would you calculate the diagonal of a cube?

Tip: When dealing with cubes, remember that all sides are equal, making the calculation of volume and surface area straightforward using simple formulas.