grammar - Would I say "I can sometimes..." or "I sometimes can..."

The answer is rather complex.

There are some rules that regulate the position of an adverb of frequency, such as: sometimes, often, occasionally, always etc.

 subject aux/be  adverb   main verb  object/place/time


  I             *often*     go swimming        in the evenings.
  He    doesn't *always*    play      tennis.
  We    are     *usually*   here               in summer.
   I    have    *never*     been           abroad.

but real usage is different for each one of them. One first distinction must be made between adverbs of frequency that can be used at the beginning (less frequently at the end) of the sentence, an adverbs that cannot.

In the example in question there is a modal verb can which functions as an auxiliary verb and therefore the correct position of the adverb should be between the aux and the main verb, as in this quote from Noel Coward:

"I'm not a heavy drinker, I can sometimes go for hours without touching a drop."

     You    can    *never*    leave
     I      can    *usually*  drink
     I      can    *sometimes* go

But,

• sometimes is one of the frequency adverbs that can be placed at the beginning of the sentence, and this is felt more natural by many native speakers, and, in addition,



• it is an exception to the rule, since it has a peculiarity of its own: it must be placed at the beginning in a negative sentence, you say:

  
  
  
  1. I do not [always / usually / often / frequently / regularly / generally] go to church.
  
  
  2. I have not [always / usually / often / frequently / regularly / generally] gone to bed after midnight.
  
  
  3. I can't [always / usually / often / frequently / regularly / generally] go for hours...
  
  

but, if you want to use sometimes in all these examples, you have to place it right at the beginning. You don't say:

"I don't sometimes go to church", "I have not sometimes gone..", "I can't sometimes go for hours", but you say: "*sometimes I don't/have not/can't..."

Any other position, including the one suggested by the general rule, is felt as wrong.

The non-negligible presence of the incorrect I sometimes can...." in the ngram quoted in another answer is due to the fact that it is quite correct in an answer: "Can you go for..." - "Sure, I sometimes can!"
If you consider it a modal verb followed by another verb, the result of the * ngram is different and gives "Not found" for the wrong form, and the other two are on the same level.

The representation of the three variants in the other ngram is misleading, since it suggests all of them are correct.

Lastly if you search for another adverb occasionally in the truncated, ambiguous form : "I occasionally can..." you get "Not found", which confirms, in a way, the peculiarity of sometimes