In my opinion, round frame sunglasses will fit your square face shape, which will soften the angles of your face. Don't get the same shape sunglasses as your face, so you should avoid anything chunky or boxy.
If you have a square face, the best type of sunglasses should be an oval or round shape which can fit your square face very well. The oval or round frame sunglasses will help soften and minimize your jaw line. So you can choose larger oval or round frames if you have a larger square face, and smaller frames for your smaller square face.
People with a square face have a wider forehead and a wider chin. For these people, they should find the right sunglasses to fit their face shape. The round or oval sunglasses will soften their facial features by making the face appear longer, so it looks not so wide. Subtle rimless frames also fit a square face well.
I don't think any kind of sunglasses will look cute an a square face. But if you are still a child, you can look for some sunglasses with decoration. Sharp detailed sunglasses will add that geometric look on your face.