It is by far the largest amount spent on political ads on the social media website on behalf of any of Scotland's 129 MSPs between October 2018 and September 2019 - and almost half the total amount invested by Holyrood politicians in such promoted messages.
Altogether MSPs spent over £9000 on targeted Facebook ads, which can pop up on people's news feeds without them having signed up or "like" the relevant page.
In the wake of the Cambridge Analytica scandal, the social media giant last year began publishing details of who places - and pays for - adverts promoting political or social issues.
The ads are often directed at particular groups, but the information published by Facebook does not give details of the target audience.
Ms Davidson, MSP for Edinburgh Central, stepped down as Scottish Tory leader last month. Her videos - one 35 seconds long, the other 28 seconds - both focused on the party's opposition to another independence referendum - were only aired for a few days each, but together cost a total of £4012.
The shorter one, active between May 21 and May 23, was seen by up to 500,000 times and the longer one, active from May 29 until June 1, was seen by up to 200,000 times.
A Scottish Conservative spokesman said: “We believe that the best way to campaign is through knocking on doors in communities across Scotland and speaking to voters directly about their thoughts and concerns.
“We promote our messaging in a number of other ways, of which Facebook is just one of them.”
A detailed analysis of promoted Facebook ads shows the social media site's users are being targeted with thousands of adverts seeking to influence their opinion of local politics.
The parties themselves spent large amounts between October 2018 and this month on their pages - Scottish Labour £12,175, the Scottish Conservatives £5,982, the Scottish Lib Dems £3,434 and the SNP £3,159.
MPs, councillors and candidates also use method to reach potential voters.
A total of £770 was spent on four targeted Facebook ads for Gordon Munro, Labour's Westminster candidate in Edinburgh North & Leith by the party. Two videos - on Labour's policy promises and the problem of fuel poverty - were each seen by up to 50,000 times, as was another post on a million people living in poverty in Scotland. A post on Councillor Munro's commitment to the local community was seen by up to 5000 times.
There were 11 promoted ads for Sheila Gilmore, Labour's Westminster candidate for Edinburgh East, costing a total of £866.
Edinburgh South Labour MP Ian Murray and the Scottish Labour Party spent a total of £148 on Facebook ads, Six, promoting his work for the constituency, started running on September 5 and have been active since. A seventh, urging people to sign a petition to save free TV licences for over-75s, ran for six days in June and was seen by up to 5000 times.
Fourteen promoted ads for Wendy Milne, Labour candidate for Linlithgow and East Falkirk, cost £1067. And Rhea Wolfson - Labour candidate for Livingston until she quit in July - had three promoted ads costing £520.
Some £779 was spent on promoted ads by City of Edinburgh Council, promoting awareness of the Leith Walk council by-election, the European Parliament elections and most recently elections for community councils. But they included an estimated £50 worth of ads which ran without a disclaimer saying who paid for them.
Others who failed to put a disclaimer on some of their ads, according to the data, included Lothian Labour MSP Neil Findlay and Labour city councillors Scott Arthur and Lezley Marion Cameron.
There is no suggestion that any of the adverts had been deliberate attempts to deceive constituents. They were all found and removed by Facebook.
The Open Rights Group, which campaigns for internet users’ digital rights, said social media had become a “key battleground for political campaigns”.
Its data and democracy officer, Pascal Crowe, said the “rules that shape our elections are ripe for reform”.
“For example, it is currently too easy to field a political advert on Facebook without revealing who is paying for that ad,” he said.
In February this year the Government announced its intention to lead a review of how online advertising is regulated in the UK.
A spokesperson for Facebook said: "Our industry-leading tools are making it easier to see all political ads on our platforms, and archives them for seven years in Facebook's Ad Library.
“People are able to report concerns to us or regulators as appropriate."