The surface area of a sphere with a radius of $6 \, \text{cm}$ is given by the expression $144\pi$ square centimeters.

To calculate the surface area of a sphere, you can use the formula:

where $r$ represents the radius of the sphere. In this case, the radius $r$ is $6 \, \text{cm}$. Substituting the radius into the formula, we have:

First, we need to calculate the square of the radius:

Next, we multiply this result by $4$:

Finally, we append the $\pi$ to our result:

Thus, the surface area of the sphere is $144\pi$ square centimeters. If you require a numerical approximation, you can use the value of $\pi$ (approximately $3.14159$):

Therefore, the approximate surface area is $452.39$ square centimeters. However, unless specified otherwise, it is generally preferable to present your answer in terms of $\pi$ for precision, especially in examination settings.