Google calendar and iOS 8 - no longer synchronizing

Question

Updated my iPhone 4s to iOS 8 and suddenly my gmail calendar is no longer synchronizing on the phone.  I've already done the restore to factory settings because after the upgrade to iOS 8, my phone lumped a bunch more files into "other" which weren't there prior to the upgrade.  I restored as new and added all my email accounts again and calendar is turned on for my gmail account.
On my MBP, my calendar is set up sans the email, and it's still all there, synchronizing perfectly.  Can't figure out what's up with the phone or why it won't work.  I've also removed the email account, re-added (for a grand total of two times) and nada.  Zip.  Zilch.  Calendar won't sync and phone will not acknowledge the gmail calendar when adding an event.
Anyone else having this problem?  I've used my work calendar on this phone for 2+ years without issue.
Thanks,

Answer 1

i realize this is a naive question, but i've never had problems with iPhones syncing before. i just gave up my 4s with iOS 5 and now have an iPhone 6, iOS 8. Everything seemed to be working well since i got the phone in late November, until a couple of days ago, and now i'm having the problem raised in this discussion and a couple of others. 
Starting a couple of days ago, i found that when i entered a new event in the iPhone calendar, it did not sync with iCal, or iCloud.  I also found that my iCloud storage was full, and eventually figured out that that was because my phone had automatically backed itself up to iCloud twice, at 2.4G each, which used up most of my 5G iCloud storage.  ??  I never had this problem before. So i thought maybe that's why the data stopped syncing. i deleted one of the backups and turned off 'back up' in the iCloud settings. But no success.
Then i discovered that Contacts were still syncing--if i entered a new contact on the iPhone, it showed up in iClound/iCal.  So only Calendar was not syncing.
Another member of these forums suggested i make sure that iCloud was set as my default calendar in Settings>Mail,Contacts,Calendar. 
in Settings>Mail,Contacts,Calendars>Calendars>Default Calendars, there are two default calendar headings. One is iCloud, and under that heading are 8 sub calendars (Home, Finance, Pets, Family, etc). The second heading is my gmail address which is my Apple ID, and under the heading there is one option, which is my gmail username.  That is checked as my default calendar.  There is no way to select iCloud as my default calendar. The heading is not selectable. If i want to choose an iCloud default calendar, my only choices are to pick one of the 8 sub calendars--which seems crazy to me. Why would i want to pick Pets, for example, to use as my default calendar? What's the point of having all those sub calendars?  i never used them as calendars. i just used them to color code the different categories. 
Anyway, i experimented with changing my default calendar from my gmail username under my gmail address heading, to one of the sub-calendars under the iCloud heading.  At random, i chose the Home "calendar."  Its color is blue. 
None of my entries of the past couple of days showed up. 
In January, i had entered three dental appointments.   They did not have a color code because i had just used the gmail username as my default calendar. They were a sort of salmon color, apparently the default color of this calendar.  I changed one of the dental appointments to Home and voila, it showed up in January where it was supposed to be.
But how crazy is this?   iCloud is forcing me to choose one of these 8 sub calendars as my default calendar, so that all of my events, regardless of their correct category, becomes part of the one category i have been forced to choose?  What's the point of having 8 different choices if only one of them can sync with iCloud?
At this point, i have tried one suggestion here, toggling my gmail account calendar off and back on.  It didn't work  I guess i will now do a reset but i am hesitating because i'm afraid i will lose data and settings and will have to put a lot more time into trying to get it set back up. It IS the main account i use and i hate to mess with it or delete it.  Why is this happening?   Everything was fine until a couple of days ago.
I went to the link posted by gosleg above.  That was a dead end because at that link, under "Select Calendars to sync to your iPhone," it only has one choice under My Calendars, and the email address (account) it shows is not my gmail address.  this has been a confusing problem i've struggled with with Google for a long time.  Before there was gmail, my google account used my then main email address, which is a roadrunner address, which i still have but don't use much.  So that is the only "calendar" that is listed under My Calendars at gosleg's link.  The check box is checked and it's grayed out.  i can't uncheck it. 
So i don't know if resetting my iPhone will even help with this. 
i only know that with my 4s with iOS 5, everything worked correctly, effortlessly, easy, and after i updated to the new phone, everything worked fine for the first 3 weeks or so, and then suddenly i started having calendar problems.
Calendar problems (possibly related):
1. entries of events in Calendar don't sync to iCloud, though contacts do
2. entries in Calendar show Greenwich Mean Time, it will enter both local time zone AND gmt, two entries on one day. Despite being set to use my local time zone in settings, it wants to make sure i know what the GMT is for all my entries.
3. iOS forces me to have alerts for Calendar entries when i don't want any. Even though in settings i have default alert time set to none, and because it's set to none, when i am entering an event, i scroll down to alerts and can see it says None, when i click add to add the even, and then open the event back up, it shows an alert for 30 minutes.  It does this every time.  i have to turn it off. 
When asked Apple about this bug, i was told i just needed to reset my iPhone.  I don't think i have ever reset any iPhone i have and it scares me.  I don't want to change it to factory settings, i don't want to have to go through everything and re-enter information. Do i risk losing anything?