1. **Stating the problem:** Evaluate the summation $$\sum_{k=1}^5 (1 + k^3)$$. 2. **Recall the summation properties:** The sum of a sum is the sum of the sums, so $$\sum_{k=1}^5 (1 + k^3) = \sum_{k=1}^5 1 + \sum_{k=1}^5 k^3$$. 3. **Evaluate each summation separately:** - The sum of 1 from $k=1$ to 5 is simply 5 because there are 5 terms. - The sum of cubes from $k=1$ to 5 is given by the formula: $$\sum_{k=1}^n k^3 = \left(\frac{n(n+1)}{2}\right)^2$$ 4. **Apply the formula for $n=5$:** $$\sum_{k=1}^5 k^3 = \left(\frac{5 \times 6}{2}\right)^2 = (15)^2 = 225$$. 5. **Combine the results:** $$\sum_{k=1}^5 (1 + k^3) = 5 + 225 = 230$$. 6. **Final answer:** $$\boxed{230}$$