Euler and Hamiltonian Cycle

Give an example of a graph that has an Euler cycle and a Hamiltonian cycle that are not identical.

I messed around with a few examples with some loops (which I'm not sure are acceptable in Euler cycle's), but I didn't get anything.

I understand the Euler cycles include all vertices and edges, and that Hamiltonian graphs include all vertices, but not all edges.

So, my idea is to insert extra vertices while keeping the degrees even, since that is a requirement for Euler cycles.