You are not likely to be handed a solution due to the potential intracies of managing that many objects in the way you describe, but here's some starter info...
To make an object follow the mouse you can make use of the mouseX, mouseY properties, as well as the object's x and y properties.
To have it happen constantly, you need to have something that constantly adjusts the values to be the same - this is often accomplished using an ENTER_FRAME event listener/handler.
To have it done smoothly can involve adding some easing to soften the motion a bit, meaning the change of position of the object relative to the mouse position is not immediate, but it lags slightly and catches up to it.
What you oughta do is search Google for tutorials using search terms such as "AS3 follow mouse easing" . Here one result from that search, and you will find numerous others as well along with it.
http://www.freeactionscript.com/tag/follow-mouse-with-easing/
Maybe after you understand how to have one object folling the mouse, you can figure out a way to make the other 16 objects follow the first object. You might think in terms of grouping the other objects and moving them as a whole unless you intend to have each one indepenetly decide how it will follow.
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