History records the Sabbath cycles reasonably well. The Jubilee cycles are more debateable, since as far as I know within Judaisn there is a single source I know of that pins it down to a single year. But let me explain both.
Numerous sources would tell us that the last Sabbatical year was 2007-2008. That puts us in the 4th year of the present 7 year cycle with the next Sabbatical year at 2014-2015. Rambam (Maimonedies) is the only source I know of that narrows down a Sabbatical year. His record of one would suggest the next one is 2015-2016. Interesting how there are a series of blood red moons scheduled for both the next coming Sabbatical year and the next coming Jubilee.
How do we know we are presently in the 1st year of the 7 year cycle that began Rosh HaShanah of 2008? For one, Modern Jewish tradition teaches us this. History also bears witness to this from several sources; Josephus, the book of Macabees and the Talmud all give us a chance to date at least one Sabbatical year and they agree on how the cycle is counted.
Josephus said Herod invaded Jerusalem during a Shabbat Year (Antiquties 14:16:2), and said his 7th year was the Battle of Actium (Ant 15:5:2, Wars 1:19:3). So that sounds like Tishri 38BC - 37BC, Tishri 31BC - 30BC, etc., were Sabbatical Years, since a Sabbath Year was in progress when he attacked that spring, so 6 years later would have been the 6th year of the 7 year cycle in Spring of 31BC. Also, 1Maccabees 6:20,49 records one for the 150th Seleucid period (164-163 BC) which comes out to an integer multiple of 7 from the record by Josephus. So Maccabees and Joseph agree.
Translating this to modern times, we get...
164-163 BC was a Sabbatical year.
38-37BC was a Sabbatical year
So was.... 31-30 AD
was a Sabbatical year, counting 7 years either from the book of Macabees or Josephus. The Talmud (Gemara Taanis 29a) tells us the temple was destroyed the year after a Shmitta, which the majority of historians put at 70AD. This also lines up with Josephus and the book of Macabees. Se we have "checkpoints" in various places from....
164-163 BC from the book of Macabees
38-37 BC from Josephus
68-69 AD from the Talmud
And all of these line up in agreement on when the 7th year are celebrated. So what about the Jubilee Year???
The Jubilee (Yovel) Cycle
Unfortunately, history is a little hazier on the Jubilee. Multiple rabbinical sources disagree on when/how to count it, and even how to apply it. One thing that the rabbis are in agreement on is that the Jubilee Year cannot be celebrated unless all 12 tribes are in the Land - otherwise - the Land cannot be returned to the tribes, which is part of what the Jubilee requirements are all about. So fuzzy problem #1 is how do you count the Jubilee year? Does the count suspend when the 12 tribes are not in the Land? Or does the count continue, but remains unobservable until they return? No one knows the correct interpretation to that question. So before I address the question of when was the last one and where is the count today, the other question is - Does it matter? Because G-d may not be going by the last count anyway. Would we start counting at year 1 if the 12 tribes were to return tomorrow? Or start counting at year 50? Or what? No one knows how G-d looks at this question. And no one is quite sure of where we are in the count either. The last observed Jubilee was before the Assyrian invasion. In fact, maybe even since the death of Solomon, when the two kingdoms split for all we know.
Rabbenu Tam (a Tosafist) writes in Talmud Gittin page 36b that the Jubilee was observed during the Second Judean Commonwealth (ended 70 C.E.). Others disagree and say that the last Jubilee observed was near the end of the First Judean Commonwealth (around 440 B.C.E). Also, see Talmud Arachin page 32b and 33a. So no one really seems to know for sure when the last Jubilee really happened.
Rambam (Maimonedies) narrows the Talmudic idea down further by saying that the destruction of the second temple happened in the 15th year of the 9th Jubilee (yovel) period. This would have meant that 55-56 AD was a Jubilee year, going by the reckoning that the Jubilee year is always the 1st year in a 49 year cycle - that is - that the 50th year is also the 1st year of another 7 year cycle. Some people think it is an extra added year - so there's another point of differing interpretations. This problem is easy to solve, because Israel's captivity lasted for 70 years, which we're told was for the failure to observe 70 Sabbaths in a 490 year period. Ifthe Jubilee year was inserted BETWEEN 7 year counts, this would not add up to 70 years. It can only result in 70 years of sabbaths for the land if the Jubilee year does not interupt the counting of the 7 year cycle, which can only happen if the Jubilee year, as the 50th year, is the first year of the 7 year cycle following seven 7-year cycles. So if Rambam was right, the next Jubilee year would be in Tishri 2015 to Tishri 2016.
Some claim Josephus mentions a Jubilee in 27-28 AD based on a footnote that appears in book 15 chapter 9 of the writings of Josephus as published by Whiston. However, upon close inspection, Josephus did not write the footnote - it was added by the editor. So the footnote does NOT carry the weight of Josephus' ancient authority. It is also not clear whether this footnote is really talking about a Jubilee year or not - it only hints at the idea. Others have theological reasons for concluding that the first year of the Messiah's ministry must have been a Jubilee year due to the wording of the quote He read of Isaiah at the start of His ministry. While it is possible that the wording was suggesting that the first year of His ministry was a Jubilee year, it may not have been. The ambiguity of the text makes that a possible, but not required way to interpret it.
If that was a Jubilee year, it would put the next one at 2036-2037. But again, I have yet to see a conclusive whether the count is suspended when the tribes are absent or merely unobserveable. So no one knows for sure, and the tabulation of the Jubilee year simply is not as easy as the tabulation of the Sabbatical year, based on historic evidence.