1. **Problem:** Find the probability of rolling a 3 twice on a number cube. 2. **Formula:** The probability of independent events both occurring is the product of their individual probabilities: $$P(A \text{ and } B) = P(A) \times P(B)$$ 3. **Step 1:** Probability of rolling a 3 on one roll is $$\frac{1}{6}$$ because there are 6 faces. 4. **Step 2:** Since rolls are independent, probability of rolling a 3 twice is $$\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$$. 5. **Answer:** The probability of rolling a 3 twice is $$\boxed{\frac{1}{36}}$$.