Weird Blur spots where object meets ground plane

in my case, its normally a problem in the Noise Reduction process..
If I do a PSD file, there I can compair the one with the Noise Reuction, and the one with out it.
And there it shows...
But cant pinpoint the problem really yet.

I've been able to reproduce the issue with a simple sequence of steps. I'm using Dimension 3.4.1 on a 2017 iMac running Big Sur 11.2. It seems to be depending on a certain combination of scene elements, materials, colors and render quality.

Here are the steps:

- open app

- add a cone

- assign material 'plastic' 

- assign color 'black'

- turn off horizontal plane

On my machine, this sequence will produce this render (PNG, High quality):

With render quality set to medium the problem is still there, seemingly in the same spot, but less pronounced. With low quality it seems to disappear completely.

Turning on the ground plane makes the error disappear - but OP had ground plane activated so that might not be the issue.

In my case I could also not reproduce the issue with a cube, but the cone had it - again, OP had cubes so the shape should not be the issue (although I originally noticed the issue on a truncated cone shape).

I then played with the materials: it looks like black plastic makes the issue become more visible. I've tried red plastic and there were no problems, as there were no apparent problems with the stock 'metal' material.

I also tried other dark gray materials like 'lined shiny paper' (sorry if this is not the correct english name, my interface is in another language) and 'ceramic tiles', and both materials presented the issue, but somewhat less pronounced than the black plastic. 

Also, while keeping an eye on the rendering itself, the problem does not appear until the very end: when the render finishes the still frame of the finished work presents the problem, but there are no traces of it during the progress.

Finally, I tried to change the camera position and the problem popped up again, roughly of the same size and intensity,  , always at the contact between the shape and the invisible plane, but seemingly in a different spot.

So, if we cross OP's and my project it seems like the only common point is the black color. 

I too have the same issue, and it's most visible when I render 'pseudo' ortho views. For example this is a render of a front view of an object: 

In this render the blur shows up in a couple of points where the object touches the horizontal plane, but the plane is turned off in the settings, so the shadows are surely nothing to do with it, as some of you suggested. 

It's shadow not bur and fixing it requires material (ground/ box) or light adjustment with the simplest fix of additional sunlight aimed at the front box face