Many people thought that the middle position would be best - that the cube size which only just fits under in the middle would not fit under anywhere else . . . . however no one has yet offered a reason for believing this . .A spreadsheet may help, though only if we can reason correctly about what the spreadsheet shows. You may like to look at a spreadsheet created for this problem.
Excel file : UnderRibbon
First you need to select a size of cube, the final column will then show the amount of ribbon needed for that cube placed at various positions along the metre length. However you will still need to reason quite carefully before you can be sure that the centre is the best position.Once you are happy about that, the Excel file has a second sheet called 'Cube in the Middle' (see the blue tab at the bottom of the page).This sheet represents a 'trial and improvement' method for a cube placed at the mid-point. You select the cube size to start at and also the size of the increase row on row, the final column will report the total length of ribbon required. That needs to be as close to 104 as you can manage without exceeding it. Although no one really accounted for their choice of the middle position, some good work was done with that position assumed.