3x4m, 45mm Log cabin with double glazed windows, not sure about the current prices (€3,500?), they seems to have dropped a lot. Add in cost of concrete base (€600?), add 200-300mm Rockwool to floor, walls, roof, clad with wood or plasterboard (you can get a heaver sound proofing plasterboard (€1,000?) , electrics own CU etc (€500?).
The 3x4m is to take into account the space lost from the insulation and it is a standard size. Those prices are just guesses. Not too sure how you would go about sound proofing the door (the standard door would not be much good) and the windows may still be a bit leaky even if double glazed. The standard double glazing some of these log cabins have is not great!