Painting a 2x2x2 Cube

Suppose you have a $2 \times 2 \times 2$ cube and you can color each of the 24 little squares one of $\color{#D61F06}\text{f}\color{#20A900} \text{o}\color{#3D99F6} \text{u}\color{#EC7300} \text{r}$ colors.

Is it possible to paint the cube so that the following holds true?

• None of the 3 squares meeting at a corner are the same color.
• None of the 4 squares meeting along an edge are the same color.
• None of the 4 squares on any face are the same color.