The information you require is available from the UNESCO Institute for Statistics.
Start here
http://data.uis.unesco.org/Index.aspx?DataSetCode=EDULIT_DS&popupcustomise=true&lang=en
and select the first field as 'Enrolment in tertiary education, ICSED 6 and 7 programmes, both sexes (number)'.
(That gives you non-postgraduate students. Use the option for ICSED 8 for postgrads).
Then select the countries you're interested in and the years. (I suggest selecting all years from 2010 onwards because it sometimes takes a few years for data to be collated and submitted). Then click 'View data'.