You may find it useful to use center=true when defining you objects. This
will place the center of all three dimension at the coordinate origin
[0,0,0].

However the general answer to you question is:

1. Translate the cube so that the point about which you wish to rotate is at
   [0,0,0].
2. Perform the rotation.
3. Translate so that the point about which you rotated is at its desired
   location.

Example:
x= 5; y =8; z=10;
translate([5,-10,15]){ // move rotated object
rotate([0,0,30]){
translate([0,-x/2,0]){ // move rotation point to origin
cube([x,y,z]);
} } }

note that the the pairs of braces {} are not required but are shown here for
clarity of the scope of each operation.

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Oops. I had meant to use
translate([0,-y/2,0]) not x/2
But this shows that you can use any point location.
Even one outside the object will work.

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I don't understand that method.

if you wished to rotate the object around its centre - y=1, once the obect
is rotate you can find where the point y-1 is relative to the new rotation
of the object, using the object's orientation vector3, and then use that
minus the same point at it's previous rotation, to translate the point to
the rotatearound position. ?!?

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ufomorace you are over thinking the problem.

If you move your object to place the center of rotation at the origin,
rotate it, then move it back by changing the sign on the x,y,z values used
for the first move, it is right back where it was, but rotated.

Nothing complicated about the math.
Yes, all the other points have a new location, but that is what you wanted.

If you now want it some where else, think about moving that center of
rotation.

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