As Galois depicted, cube doublication cannot be constructed via unmarked straightedge and compass. Any solution to this problem should make cubic extension or above. I have already known this method to construct any angle trisection via unmarked T-shaped ruler and compass: https://en.wikipedia.org/wiki/Angle_trisection#With_a_right_triangular_ruler where T-shaped ruler is this, or you can use set square instead: https://en.wikipedia.org/wiki/T-square
But I cannot find a way to construct an conchoid of a straightline as neusis construction do: https://en.wikipedia.org/wiki/Doubling_the_cube#Using_a_marked_ruler
I know only one special technique to use unmarked T-shaped ruler: one arm passes through one given point P, another arm keeps tangent to one point Q on given curve C. Moving point Q, so the right angle of T-shaped ruler O can draw a curve. I think this curve fits this difination: https://en.wikipedia.org/wiki/Pedal_curve
I have proved the conchoid of a circle if given point P is on circle constructed by neusis construction is equal to curve drawed by unmarked T-shaped ruler on a circle with the technique above. But I still cannot find a way to doublication the cube.
There is a proof for not constructing that length via angle trisector: http://math.fau.edu/yiu/PSRM2015/yiu/New%20Folder%20(4)/Downloaded%20Papers/AMMGleason1988.pdf but I believe that unmarked T-shaped ruler is much more than angle trisector.
But is it possible? If possible, how can I draw it?