To find the unit rate of cupcakes per box, divide the total number of cupcakes by the number of boxes.
\[ \text{Unit rate} = \frac{\text{Total cupcakes}}{\text{Number of boxes}} = \frac{36 \text{ cupcakes}}{3 \text{ boxes}} = 12 \text{ cupcakes per box} \]
So, there are 12 cupcakes per box.