* U.S. inventories fall 8.1 million barrels -API
* EIA cuts U.S. oil production forecast for 2018
* European refineries boost crude intake in June
* European stocks of diesel and other oil products slid
* Goldman Sachs warns of oil below $40 per barrel
* Saudi Arabia produces a little more oil in June than OPEC target (Adds API numbers and context)
NEW YORK, July 11 (Reuters) - Oil prices climbed more than 2.5 percent on Tuesday along with rising heating oil futures on reports showing cuts in U.S. oil production and declines in U.S. crude and European product stockpiles.
U.S. crude stocks plunged almost three times more than forecast in the latest week, while gasoline inventories decreased unexpectedly and distillate stocks built, industry group the American Petroleum Institute said Tuesday.
Crude inventories fell by 8.1 million barrels in the week to July 7 to 495.6 million, compared with analysts' expectations for a decrease of 2.9 million barrels. Crude stocks at the Cushing, Oklahoma, delivery hub fell by 2 million barrels, API said.
Benchmark Brent futures rose 64 cents, or 1.4 percent, to settle at $47.52 a barrel. U.S. West Texas Intermediate crude also rose 64 cents, or 1.4 percent, to settle at $45.04 per barrel.
After the close and the supportive API data, Benchmark Brent futures rose $1.25, or 2.7 percent, to $48.12 a barrel. U.S. West Texas Intermediate crude rose $1.31, or 2.9 percent, to settle at $45.71 per barrel.
U.S. heating oil futures, meanwhile, gained 1.6 percent on Tuesday, boosting the products crack spread <CL321-1=R>, a measure of refinery margins, to the highest since late May.
European refineries increased crude oil intake in June, but stocks of oil products, particularly diesel, slid, Euroilstock data showed on Tuesday.
"That tells you demand globally is a lot stronger than people thought it was going to be and that is having a net positive effect on heating prices," said Scott Shelton, energy specialist at energy brokerage ICAP in Durham, North Carolina.
In a separate report on Tuesday, EIA projected U.S. crude oil production in 2018 will rise by less than previously expected.
Traders noted Tuesday's crude price declines were mitigated by reports Saudi Arabia exceeded its OPEC production target and notes from banks lowering oil price forecasts for this year and 2018.
BNP Paribas slashed its forecasts for Brent by $9 to $51 a barrel for 2017 and by $15 to $48 for 2018. Barclays cut its 2017 and 2018 Brent forecasts to $52 a barrel for both years from $55 for 2017 and $57 for 2018.
Crude prices remain about 16 percent below 2017 opening levels despite a deal led by the Organization of the Petroleum Exporting Countries to cut production from January.
OPEC agreed with Russia and some other major exporters to cut output about 1.8 million barrels per day until March 2018. But production elsewhere has risen as OPEC has held back.
U.S. oil production <C-OUT-T-EIA> has jumped more than 10 percent over the last year to 9.34 million bpd. Nigeria and Libya, OPEC members exempt from production limits, have also increased output.
Saudi Arabia's oil production in June rose to 10.07 million bpd, putting it about 12,000 bpd over its OPEC output target.
Without a significant fall in oil inventories or a decline in U.S. drilling and production, Goldman Sachs said U.S. crude could drop below $40 per barrel.
(Additional reporting by Scott Disavino in New York, Christopher Johnson in London and Henning Gloystein in Singapore; Editing by Diane Craft and Lisa Shumaker)