Mods can describe the reason, and in my opinion they should. If they don't do it, it is evil. Although they aren't needed to do it, in my opinion it is at least questionable behavior to miss it. Furthermore, it opens the door before misuse accusations. Their template in these cases looks like:
"You were bad, you are not a nice guy, you posted insulting comments
...examples of your insulting comments...
These comments were removed. Furthermore, you were so evil that I ban
you for a year."
Although it is formulated more politely and with perfect English, but it is the essence.
As they cage somebody, they can select a list of templates, so they don't have to bore too long with a cage.
Also I experienced lately that I got a (similarly short) caging but without citing the real posts, why I was so bad. I hope, it won't become a new custom. If the mod doesn't cite the reason, it makes himself unattackable on an unfair way.
Posts leading to a suspension are also posts should be removed by their content. Thus, you can't see them, except the rare cases if you have 10000 reputation points on the site, which makes for you visible to see removed posts (but note, only mods can see removed comments, not even the 10k+ users). This is a highly problematic thing here on the SE, here you can downvote my related answer arguing against this.
But don't worry on a week long suspension, it is essentially nothing. It could be even far worse. Mods can only suspend anybody at most for a year; and only for their site. They tend to give the suspension times incrementally. The message you've now got will remain forever attached to your account, and it will be visible by the CMs and mods. Your next suspension will be at least 1 month.
All cage decisions are automatically reviewed by the CMs, but they mostly don't intervene. If you think it was really evil, you can contact them on the
/contact URL of your page, but don't expect earth-shaking changes, particularly in the case of such short bans.
CMs can provide network-wide or much longer cages; an example. In the database record describing your account there is a date field for that, the maximal value is
9999-12-31. It is long, but the suspensions are only temporary, so we only have to wait.
If your cage happened not on a comment, but on an answer or question: you can still read your own deleted posts (you can even edit them), although the SE intentionally doesn't provide any way to find them. You have to remember its link, or to find it is its browser history. Only mods and yet higher powers can list the deleted posts of others (and listing the deleted comments is possible only with db-access, as far I know).