Using the command line to enter the Start Corner, Length, Width and Height doesn't draw the box at the correct start corner but adds an offset to it. I believe this problem is within the engine as it is also a problem in Progecad.

Which version of Icad are you running?
I just tried using 13.0 and no issues found.

Version 13.1 is the version I was trying it with.

I used metric units template.
Set View to Above right front.
Selected 3D Solid Box
prompt Specify first corner of box or [Center]:
reply 10,10,0
prompt Specify other corner or [Cube/Length]:
reply L
prompt Specify length: <25.000000> :
reply 40
prompt Specify width:
reply 50
prompt Specify height or [2Point] <50.0000>:
reply 30

3D solid box is drawn but at the first corner coordinates 10,15,0, which is wrong.
I have tried it several times and it never draws the 3D solid box at the correct first corner point.
The 3D mesh box works ok.

Try repeating the sequence, but first draw a line from 10,10,0 to anywhere.
Then measure between the line endpoint and you cube origin.

Works for me in 13.0

It works for me in 13.1 too.
When using the command line, please turn off the snap setting.

It operates fine for me in version 13.1 as well.