1. The problem asks us to translate the graph of the parent function $y = x^3$ to the graph of $y = (x + 1)^3 - 4$. 2. The parent function is $y = x^3$, which is a cubic curve passing through the origin $(0,0)$. 3. The transformation involves two steps: a horizontal shift and a vertical shift. 4. The function $y = (x + 1)^3 - 4$ means we replace $x$ by $x + 1$, which shifts the graph horizontally to the left by 1 unit. 5. Then, subtracting 4 shifts the graph vertically downward by 4 units. 6. So, the graph of $y = x^3$ is translated 1 unit left and 4 units down to get the graph of $y = (x + 1)^3 - 4$. 7. In summary, the translation vector is $(-1, -4)$. Final answer: The graph of $y = (x + 1)^3 - 4$ is the graph of $y = x^3$ shifted 1 unit left and 4 units down.