Google Cache/Indexing (are not interlinked with one another)
Google's cache service normally updates quicker than the actual indexing of pages, but sometimes can be slower. The cache service and indexing service are independently updated and do not work with one another as you would expect, so for example say Google[BOT] visits your site and crawls data it is then uploaded to Google and then the indexing service needs to read that data into its engine, same as the caching. So in other words its NOT REAL TIME - and indexing has nothing to do with the cache service. However backwards this sounds I'm sure that Google has valid reasons for doing it this way.
If you would like to know the exact reasons why they do this maybe someone can answer but in my honest opinion knowing why what change this outcome, none the less you may get a Google answer from http://productforums.google.com/forum/#!categories/webmasters/crawling-indexing--ranking
It's Worth Noting
It is common for a lot of sites to be updated from several to even weeks depending on how important Google sees your site. There is little evidence that resubmitting your site actually speeds up this process, the normal way Google works is that it priotized its resources what it believes is important to update. For example BBC site will most likely get updated with a few hours or just the day, while the average joe site will take a few days to couple of weeks.
Speeding up the Process
If you want to speed up the process of having changes being updated then you need to update your site more regularly Google will take note of this so for example if you update your site every 2 days, Google will learn that every 2 days you update your site and is 'MORE' likely to return for those changes. Sometimes back linking can cause a crawl as well. But best advice is to be patience with Google ;)