As a noun, there is a cure for
something, as you note, in sentences like these:
"¢ Punishment can never be an effective cure for
acute social problems.
"¢ The magic cure for
inflation does not exist.
"¢ The master web site concerning the cure for
common colds using zinc lozenges. www.coldcure.com/
"¢ ... The remedies do effect a cure for
ringing in the ears- the total elimination of the ringing ear noises in most cases or at worst, a substantial reduction of ... www.doctor-brom.com/
As a verb, "cure" is used with of
-- often with the past participle -- to express the separation (of someone or something) from a problem:
"¢ Now doctors believe they have cured him of
"¢ The experience was a detestable ordeal and it cured him of
any ambitions to direct again.
"¢ Toastmasters cure fear of
public speaking through public speaking. Darren J. Clarke, News Office April 10, 2002. Whether they freeze ...
"¢ DH Lawrence: I cannot cure myself of
that most woeful of youth's follies - thinking that those who care about us will care for the things that mean much to us. ... www.brainyquote.com/quotes/quotes/d/dhlawren151175.html
As a verb, "cure" is not followed by any preposition when there is no mention of the malignant cause the object will be separated from:
"¢ An operation finally cured his shin injury.
"¢ We need to cure our environmental problems.
Example sentences are from the Collins COBUILD English Dictionary (HarperCollins, 1995), except for those with URLs, which are from Google.