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We present a new ``universal property'' of entropy, that is the ``entropysum'' relation of black holes in four dimensional (anti-)de-Sitter asymptoticalbackground. They depend only on the cosmological constant with the necessaryeffect of the un-physical ``virtual'' horizon included in the spacetime whereonly the cosmological constant, mass of black hole, rotation parameter andMaxwell field exist. When there is more extra matter field in the spacetime,one will find the ``entropy sum'' is also dependent of the strength of theseextra matter field. For both cases, we conclude that the ``entropy sum'' doesnot depend on the conserved charges $M$, $Q$ and $J$, while it does depend onthe property of background spacetime. We will mainly test the ``entropy sum''relation in static, stationary black hole and some black hole with extra mattersource (scalar hair and higher curvature) in the asymptotical (anti-)de-sitterspacetime background. Besides, we point out a newly found counter example ofthe mass independence of the ''entropy product'' relation in the spacetime withextra scalar hair case, while the ``entropy sum'' relation still holds. Theseresult are indeed suggestive to some underlying microscopic mechanism.Moreover, the cosmological constant and extra matter field dependence of the``entropy sum'' of all horizon seems to reveal that ``entropy sum'' is moregeneral as it is only related to the background field. For the case ofasymptotical flat spacetime without any matter source, we give a note for theKerr black hole case in appendix. One will find only mass dependence of``entropy sum'' appears. It makes us believe that, considering the dependenceof ``entropy sum'', the mass background field may be regarded as the next orderof cosmological constant background field and extra matter field.

The "universal property" of Horizon Entropy Sum of Black Holes in Four Dimensional Asymptotical (anti-)de-Sitter Spacetime Background