How to automatically delete spam on the default mailboxes on the hosting?

Create left gmail and upload this mail without saving it on the server. At the same time spam will filter out and you can even read what remains.

email hosting — let him close the drawer. I closed my wishing in my time.

I'm not sure that such function is provided. Try to configure any email client to collect emails from that mailbox using pop3, with the flag "delete from server".
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In your email client to delete these emails filter on the to field. Or just put in a separate folder.

Theoretically, if the editor of the DNS to create an MX record to specify the localhost as the mail handler, mail and spam from the outside just won't come.
Practically, your sites can send mail, and letter-mistakes will fall in these bins.
And neadkvaten spammers can send mail directly via the A-records i.e. the same server that serves the website.

If you mean that любоеимя@domen.com mail is going into the default Inbox, simply change the setting in "mailbox to collect the mail." Or delete it.
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If the box is needed, but prevent spam — SpamAssassin nastraivat need to otmenyal spam instead of moving it anywhere.

If the box cannot be removed, then it is often possible to limit the size.
Make it minimal and let it overflow.

A little perverted method, but it is possible to deliver Mail For the Domain from Yandex or Google Apps — let the spam accumulate there, and you have the boxes name@example.com will.