We study the white dwarf (WD) cooling sequence of the Galactic Globular Cluster (GGC) NGC 2808 by using deep near-UV data from the Hubble Space Telescope and theoretical models, to investigate if this cluster hosts an excess of WDs. Excess in WDs is a rare phenomenon that has been found to exist only in a few GGCs. We compared star counts from different evolutionary phases on the near-UV color-magnitude diagram to evolutionary times predicted by BaSTI models. The investigation was carried out over a region within a radii of 1.5 of the cluster center and a region of similar dimension located 5 away. We find a WD excess of 60 - 70% when comparing star counts and evolutionary models of the WD cooling sequence to the main-sequence turn-off, and by using different values and fractions of Helium enhancement. This excess decreases to 30 - 40% when the WD cooling sequence is compared to the horizontal branch. The WD excess is slightly larger in the internal field that covers the cluster center; however, the difference with the external field is compatible within the uncertainties. We argue that this excess is possibly related to the existence of SCWDs and Helium-core WDs in NGC~2808, and might be directly associated to the extended blue horizontal branch of this GGC.

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