#### Answer

The function is only symmetric with respect to the y-axis.

#### Work Step by Step

Step 1. Replacing $x$ with $-x$, we have $(-x)^2+y^3=7$, which gives $x^2+y^3=7$; thus the function is symmetric with respect to the y-axis.
Step 2. Replacing $y$ with $-y$, we have $x^2+(-y)^3=7$, which gives $x^2-y^3=7$; thus the function is not symmetric with respect to the x-axis.
Step 3. Replacing $x$ with $-x$ and $y$ with $-y$, we have $(-x)^2+(-y)^3=7$, which gives $x^2-y^3=7$; thus the function is not symmetric with respect to the origin.