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http://www.tradingeconomics.com/country-list/gold-reserves

For example, some of German's gold reserves are stored in US central bank as explained in https://en.wikipedia.org/wiki/Gold_repatriation:

The gold in the U.S. was earned by West Germany through trade surpluses in the 1950s and 1960s and never moved it out of the United States due to fear of invasion by the Soviet Union.

In the case, does the 8133 tonnes gold reserves in US include the gold liability to other countries?

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No.

The $8,133.5$ tonnes of gold, i.e. $261,498,926.230$ fine troy ounces, of the U.S. Government owned gold reserve is detailed in a monthly status report produced by the US Department of the Treasury, with the latest figure being for August 31, 2016.

The weight and notional value of $\$11$ billion (based on a statutory rate of $\$42.2222$ per Fine Troy Ounce) have change by very small amounts in recent years, I would guess related to selling gold coins and buying stock to make them. For example the total in January 2012 was $261,498,899.316$ fine troy ounces, a difference of about $27$ troy ounces from the current figure.

Gold belonging to other countries are stored in the US, particularly in New York as being convenient for the market and for transport. But this is not counted in the US Treasury report.

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