An Air Carrier Captain reported the aircraft burned over 1000 LBS more fuel than planned in the flight plan due to a fuel leak or incorrect flight planning.

Narrative

Aircraft X; ZZZ-ZZZ1 Day 0; Aircraft X scheduled departure time XA03-XC01; actual XB05-XD10. The inbound flight arrived late from ZZZZ with a longer than average turn around time. Aircraft X had 2 MELs and 1 CDL: XX-XX-XX-13; XX-XX-XX-2 and XX-05 respectively. Dispatch release ramp fuel on board 18.7; actual 18.9. Min required at takeoff 17.4. Remaining fuel at ZZZ1 5.5 with a cost index of 16.Once we pushed off there was no undue delay departing ZZZ; doubtful we used all 600lbs of taxi fuel for the short 2 engine taxi to XXL. We completed the Line Up checklist with fuel on board (FOB) well above MIN; 18.5 if memory serves; it was a long duty day. After departure we were quickly cleared on our flight planned route with a left turn direct ZZZZZ. With benign weather and near direct flight plan to ZZZ1; I expected our estimated fuel on board (EFOB) on the FMS to be higher than the 5.2 it was indicating. Winds aloft were very close to forecast. With the extra fuel above MIN I expected and usually see the commensurate increase in EFOB from planned. In this instance; planned remaining fuel 5.5; expectation 6-6.5 EFOB. I had initially selected a cost index of 30 to make up a little time enroute; with a 2:44 flight time the EFOB between CI 16 vs CI 30 was only a 1-200lbs. After reaching cruise; I noticed the EFOB started decreasing to under 5.0 and returned to CI 16; which only slightly increased our EFOB.A couple of shortcuts straightened our already nearly direct route with only minor vectors from ATC for traffic. I did our first fuel hack at ZZZ2 roughly 30 minutes into the flight; planned FOB 14.1; actual 13.6; 500lbs down. Now I'm getting concerned; we should be planned +500; certainly not short. I looked at the fuel page; tank levels were balanced and when adding FOB to fuel burned totaled 18.2; not much different from the roughly 18.5 fuel we departed with. Subsequent fuel hacks revealed a continuing fuel deficit; at our rough equal time point we were down 800 lbs; FMS EFOB 4.5. Each time adding FOB to fuel burned stayed consistent at 18.2 with balanced tanks. By the time we started the arrival we were down 1000 lbs and FMS EFOB 4.3. The fuel predict page indicated reserve fuel at 3.5; planned final reserve at 3.0. Right before we switched runways from 11 to 02; EFOB briefly hit 4.1.After conducting a visual approach to X; actual FOB at touchdown was 4.3. I wrote up the aircraft for a suspected fuel leak after my First Officer did a post flight walk around; there was a fuel smell from the left wing but that could've been attributed to other fuel related equipment near the wing. After thinking about additional reasons why there was such a discrepancy in planned fuel (plus) vs actual burn; one possibility the performance factor of 2.4% wasn't accurate with the engines burning more fuel than normal or the listed MELs/CDL had a larger than usual performance penalty; even though no penalties were indicated. Either way I felt something was amiss with the aircraft; it's the first time I've flown essentially a VFR flight per the flight plan and be down more than 1000 lbs per the flight plan when FOB at takeoff indicated we'd be handsomely above all the planned fuel numbers.