There are two easy ways, one more obvious than the other. (If I missed the point of what you wanted, let me know.)
1) Make a Replicator
Start with your square shape - Outline - White border color
With the Square shape selected in the layers list, type L to create a Replicator (or select Replicate from the Object menu)
Set the Replicator Shape to Circle
Radius to about 360 (whatever you want)
Points to about 36 (give or take)
If you want the rectangles to "follow the circle shape" -- check the Align Angle box
Set the Color Mode to Over Pattern and create your color changes "over time"
You will need to add a Behaviors > Replicator > Sequence Replicator
In the Sequence Replicator behavior inspector,
Parameter > Add > Opacity
Set the Opacity to 0
Set the Sequencing to From
Play
To create an animation so that the "drawing on of squares" moves around the circle:
Add a Behaviors > Basic Motion > Spin behavior and set the Spin Rate to 36º (if you project is 10 seconds long — this value will need to be changed for different length projects).

Method 2:
Draw your square shape - Outline - Border Color white.
Draw the Circle you want to animate the squares around.
For the Circle, in the Shape > Style inspector, set the Brush Type to Image.
In the Brush Source well, drag and drop the Rectangle (square shape) from the Layers List.
Set the Width to around 100 and the Spacing to about 80%.
Add a Behaviors > Shape > Write On and in the Write On behavior inspector, set the Direction to Reverse.
Go back to the Shape inspector and select the Stroke tab of the inspector.
Set the Stroke Color Mode to Color Over Stroke.
For the Color Over Stroke, create you Gradient "over time" color.
Look down the list and find Align Brush Angle and select the checkbox.
Add a Behaviors > Basic Motion > Spin behavior and set the Spin Rate to -36º. (This animation will move in the opposite direction to the one above:)

There are other ways to do this sort of thing... experiment 😉