$ \forall n \in N$ edges of $K_{2n+1}$ can be partitioned to hamiltonian cycles.

Question

A hamiltonian cycle is a cycle which visits each vertex of the graph exactly once.
A hamiltonian path is a path which visits each vertex of the graph exactly once.

We need to prove that:

1-$ \forall n \in N$ edges of $K_{2n+1}$ can be partitioned to hamiltonian cycles.

2-Then show that edges of a $K_{2n}$ can be partitioned to hamiltonian paths.

Note : We already know that every complete graph has a hamiltonian cycle. The problem here is that the question doesn't want just one cycle. I am not sure how to pove that such a partitioning exists.

Any help will be useful!

Thanks in advance.