Universities and colleges in England face "significant funding shortfalls and heightened uncertainty" due to the Covid-19 pandemic, a report warns.
The Institute for Fiscal Studies says fewer overseas students, potentially higher dropouts and high pension costs are a financial risk for universities.
Further education colleges still face budget pressures, despite a £400m cash boost, says the report.
The government says it understands this is a "challenging time" for the sector.
The IFS report on education spending in England, which was funded by the Nuffield Foundation, warns that universities could be exposed to a range of financial losses, such as falling international student numbers and more students failing to complete their degrees.
"By far the largest source of financial risk for universities is pension costs," it says.
"New figures suggest the additional cost to universities of meeting existing pension promises may well be as high as £8bn, or double our previous estimate of around £4bn."
Universities could only reduce this by "taking on more risk, making further reductions in the pensions provided by the scheme, big rises in employees' contributions" or a combination of these.
But such measures are likely to be controversial - last academic year, lecturers went on strike over pensions, as well as pay and conditions.
The IFS also says student numbers in further education colleges and sixth forms are likely to increase this year, partly due to rising numbers of young people and partly due to "unusually high GCSE results" and significant reductions in training and employment opportunities.
While England's colleges and sixth forms will receive an extra £400m this year, "exceptional rises in student numbers could still generate a real-terms fall in funding per student".
They will also face challenges around educational catch-up, but may also "need to expand to accommodate extra students as apprenticeship and employment opportunities dry up", the IFS says.
The report also raises concerns about early years provision, saying settings are likely to be "much more financially exposed, both to the second lockdown and more broadly to a rather slow and incomplete return of demand for childcare".
While early years providers "were financially well protected" during the first lockdown by the government's commitment to continue to fund the free entitlement hours, a reassessment of this funding in January 2021 could prove problematic for providers.
Report co-author Ben Waltmann said there had been speculation in the summer that universities would need a financial bailout.
"In the end, student numbers have held up better than expected, but universities still face financial risks from no-shows or higher-than-usual dropout, as well as reductions in other income streams," he said.
"By far the biggest source of risk now appears to be the large deficit on the main university pension scheme, which has increased from £3.6bn in March 2018 to a monumental £21.5bn in August 2020, according to the latest preliminary estimate.
"With contributions already at more than 30% of earnings, it is hard to see how a deficit on this scale, if confirmed, could be evened out without further cuts in the generosity of the scheme."
Co-author Imran Tahir said the government had made transforming further education colleges a big priority, pledging £400m in extra funding at the 2019 Spending Review.
He said this could be "the first real-terms increase in spending per student for about a decade".
"However, student numbers could have risen dramatically more than expected due to a reduction in training, apprenticeship and employment opportunities, on top of population growth.
"If there is no additional funding forthcoming, planned real-terms increases in spending per student could be mostly - if not entirely - eroded."
A spokeswoman for the Department for Education said the government had introduced a range of support.
"We have protected grant funding for further education, worth over £3bn for a full year and increased education and training investment this year for 16-19 year olds by an additional £400m.
"We also brought forward over £2bn worth of tuition fee payments for universities and announced a major package of £280m to stabilise research funding."
But Geoff Barton, head of the head teachers' union ASCL, said colleges were often "treated by the government in terms of funding as a Cinderella service".
Bill Watkin, chief executive of the Sixth Form Colleges Association, said the reduction in funding had led to "courses being cut, support services reduced and extra-curricular activities removed for 16 to 18 year olds across the country".
The £400m investment "was a welcome step", he said, "but was only a one year deal following a decade of neglect."