My friend has asked me this question. I have no idea how to answer, but I think the question is interesting enough to be noted here:
Consider 3 pieces of wire (not necessary of equal length). Is it possible to construct a cube from them by only bending or pasting them ?? (no cutting is allowed)
No. The cube has eight vertices of odd degree. If the wire is not doubled up anywhere then each vertex must be an endpoint of one of the pieces of wire, since otherwise the wire would go out for each time it goes in nd the degree would be even. Three pieces of wire have only six endpoints.