It looks like you're providing a mathematical expression or function involving $z$, $x$, and $y$, but the notation is unclear. Let me try to parse it properly. Based on what you've written, it seems the function $z(x, y)$ might be intended as:

$z(x, y) = 2x^3 + 6x^2y + 16y^3 - 3x^2 + 6y$

Let me know if this matches your intended expression. If so, I can assist with tasks like differentiation, simplification, finding critical points, or any other related calculations.

Would you like to proceed with:

1. Partial derivatives of $z(x, y)$?
2. Simplification or factored form of $z(x, y)$?
3. Evaluation of $z(x, y)$ at specific points?
4. Solving $z(x, y) = 0$?
5. Any other operation?

---

Tip:

When writing equations, use parentheses to group terms clearly (e.g., $2x^3 + (6x^2y) + \dots$). This ensures accurate interpretation.