I bought my Android last January and I forgot to charge it for 8 hours.
What will be the effect on my Android and battery life? ( battery type is Lithium Polymer)
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Firstly, Li Polymer has the same charge/discharge characteristics as Lithium ion, the underlying chemistry being the same. For more information see Li-Ion vs Li-Poly, plus how do Lithium batteries work anyway?
When the phone is marketed, manufacturers, typically charge the battery to around 40% as you may have noticed. This is good for battery longevity and ensures battery degradation does not occur on storage. See BU-702: How to Store Batteries for better understanding
There isn't a valid reason for charging the batteries for xx hours before first use or to charge till 100%. It is yet another charging myth , see misconception # 6
So, not charging for 8 hours does not matter and your battery is pretty much in the same shape as it was.
See BU-415: How to Charge and When to Charge? for a general understanding of charging "do's and don'ts)
Additional information on this site that would help you care for your batteries