To add color circles to any "Filter Products by Attribute" default WooCommerce widget follow the steps:

1. In Products → Attributes add a "Color" attribute (the name can be different).
2. In Products → Attributes → Color add some colors like "Black", "Blue", "White" etc.
3. In Products → (each product) go to "Attributes" section and assign colors to your products.
4. In Appearance → Widgets add "Filter Products by Attribute" widget to your shop sidebar.
   1. Preferred operator is "OR".
   2. Attribute to filter by is "Color".
   3. Now you have a working colors filter but on the front-end it only shows color labels without color circles.
5. Install "BLK Color Filters" plugin.
6. In WooCommerce → BLK Color Filters specify colors for your labels (only for the "Color" attribute).