What are the i,j,k components of a 3d mesh on plot.ly (online)? A 3d Mesh on plot.ly online graph maker (https://plot.ly/create/#/) takes 3 mandatory variables (X, Y, Z) and 3 optional variables (I, J, K).
I understand that if I want to draw a cube that I then have to use the IJK-variables, since without them nothing will be drawn.

After some googling I found that with i, j, k you can represent vectors. Though I do not understand how in the following examples they correspond to the XYZ values, so that a cube can be drawn.
There are several examples of cubes and cuboids on plot.ly, all of which share the same i, j, k, values. 
f.e.
https://plot.ly/create/?fid=RPlotBot%3A3933#/

https://plot.ly/create/?fid=markope%3A143#/

Taking the first link as an example:

x   y   z       i   j   k
0   0   0       7   3   0
0   1   0       0   4   7
1   1   0       0   1   2
1   0   0       0   2   3
0   0   1       4   5   6
0   1   1       4   6   7
1   1   1       6   5   1
1   0   1       6   2   1
                4   0   5
                0   1   5
                3   6   7
                2   3   6


This will draw a normal cube.
When I try my XYZ-coordinates, however, it will draw following:


My xyz-coordinates are:

x   y   z
25  25  65
25  55  65
55  25  65
55  55  65
25  25  80
25  55  80
55  25  80
55  55  80


How can I calculate the according ijk-values so that I get a cuboid? Any tips or links to resources?

The official tutorial for a 3d mesh on plot.ly online graph maker only mentions the ijk-values, doesn't explain them though.
Most mesh drawing tools use triangles to draw meshes, for technical reasons.

You could simply specify the coordinates of the three vertices of each triangle, but that is a bit wasteful in terms of memory.

What is done in many places is to specify a list of points in space, with their coordinates, and then specify a list of triangles, using indices of the points in the first list. 

The exact same thing happens here. The x,y,z parameters form a list of points. The I,j,k parameters indicate triangles, using IDs in the list of points. 

Have a look at the function documentation for more details:
https://plot.ly/python/reference/#mesh3d