Does university have any cultural mission? I am asking this question, as my previous question was closed because of being opinion-based. This made me wonder if there is a conceptual mission for higher education or not?

In most European countries, public universities receive the majority of their budget from the government, as higher education is somehow a public service, and responsibility of the government.

Imagine that all universities in Germany or Sweden decide to abandon any social activities of students. Sell all big campuses and buy modern buildings and only run the educational classes. Then, do the government, parliament, tax payers accept this policy? Is it the university's decision to make or universities have social and cultural responsibility for the society.

It was an exaggerated example, but my point is that: 

Are universities simply business entities (even not for profit) to provide a service (which is educational courses) against the money they receive (from tuition or aid).

OR

They have social responsibility to make better citizens beside the professional training.

NOTE: I understand that an urban university may only offer education for a specific range of audience (for example students busy with jobs), but is it acceptable from the fundamental concepts of higher education that a university totally eliminate social activities by assuming that the main responsibility of a university is just providing high quality education.
Almost all universities have a larger mission than simply provision of educational courses.  For example, consider the mission statements of two very different publicly funded American institutions:


The University of Texas System, in addition to education, aims to develop ethics and morals, appreciation of arts and culture, and prepare "educated, productive citizens who can meet the rigorous challenges of an increasingly diverse society and an ever-changing global community"
Bunker Hill Community College is much closer to the "pure skills" model, but still also aims to provide community leadership and to ensure that "no eligible student shall be deprived of [education] because of an inability to pay tuition and fees."


In both cases, the university is explicitly aiming to promote social and cultural change towards a society in which most people would generally prefer to live (even though the particular goals of each are different).

Now, mission statements are one thing, reality is another.  Every university's leadership decides how it wants to interpret and/or modify its mission statement. Universities also generally have some sort of board overseeing it, which will attempt to guide and shape the university's actions.  This is where, especially with public universities, there is often a great deal of fighting about the university mission and policies around it.  For example, conservatives who are uncomfortable with the cultural broadening provided by universities often argue that a university should "just stick to teaching skills."  In general, however, the faculty and leadership of most universities tend to promote some sort of cultural mission, even if some are very different than most.