Network operators must continuously scale the capacity of their optical backbone networks to keep apace with the proliferation of bandwidth-intensive applications. Today's optical networks are designed to carry large traffic aggregates with coarse-grained resource allocation, and are not adequate for maximizing utilization of the expensive optical substrate. Elastic Optical Network (EON) is an emerging technology that facilitates flexible allocation of fiber spectrum by leveraging finer-grained channel spacing, tunable modulation formats and Forward Error Correction (FEC) overheads, and baud-rate assignment, to right size spectrum allocation to customer needs. Virtual Network Embedding (VNE) over EON has been a recent topic of interest due to its importance for 5G network slicing. However, the problem has not yet been addressed while simultaneously considering the full flexibility offered by an EON. In this paper, we present an optimization model that solves the VNE problem over EON when lightpath configurations can be chosen among a large (and practical) set of combinations of paths, modulation formats, FEC overheads and baud rates. The VNE over EON problem is solved in its splittable version, which significantly increases problem complexity, but is much more likely to return a feasible solution. Given the intractability of the optimal solution, we propose a heuristic to solve larger problem instances. Key results from extensive simulations are: (i) a fully-flexible VNE can save up to 60% spectrum resources compared to that where no flexibility is exploited, and (ii) solutions of our heuristic fall in more than 90% of the cases, within 5% of the optimal solution, while executing several orders of magnitude faster.