I don't know of any example where the Buddha actually said "life is suffering".
The first noble truth is simply "This is the truth of suffering." Nowhere in the enumeration of what is suffering does it refer to life.
"Life is suffering" isn't listed in fakebuddhaquotes; but it is the first item in a list of "Misunderstanding that arises from the teachings" on this page titled, "Common Buddhist Misunderstandings".
a) Life is suffering
The Buddha told us that "Life is Suffering". One who does not understand the Truth of this may think that life is meaningless and become negative and pessimistic. Actually, this theory is commonly misunderstood. People in society and even some Buddhists are trapped in this wrong and gloomy view.
To be honest this one actually claims that
The Buddha told us that "Life is Suffering" though it then goes on to say that's misinterpreted.
The article is translated, perhaps from Chinese, in case that's relevant?
In this Article titled Life Isn't Just Suffering, Thanissaro Bhikku wrote,
You've probably heard the rumor that "Life is suffering" is Buddhism's first principle, the Buddha's first noble truth. It's a rumor with good credentials, spread by well-respected academics and Dharma teachers alike, but a rumor nonetheless. The truth about the noble truths is far more interesting.
In a comment to another answer, you wrote,
For example sukkhavedanā or "pleasant sensations" are also, in the broadest sense, dukkha! PTSD doesn't cope with that observation. For example: Nāññatra dukkhā sambhoti, nāññaṃ dukkhā nirujjhatī’’ti "Nothing other than dukkha arises, nothing other than dukkha ceases." This does not make sense if dukkha simply means "misery" or "sorrow". Because also we have experiences like ānanda, pamoda, pīti, sanutuṭṭha, sukha sukhita, somanassa.
Looking at the context of that quote (i.e. Vajira Sutta) I think that's a reference to dukkha as a characteristic of existence.
Given texts like Sabba Sutta perhaps it's reasonable (if a bit loose) to summarize "the aggregates" as "life" — and then the word "suffering" obviously comes as a translation of dukkha, though in context it might mean something else.
I suspect that (as well as being defined in isolation) the meaning of dukkha as it's used in a Buddhist context might be hinted at, defined, informed by or inferred from the second and third noble truths.
And that Vajira Sutta isn't easy to understand in isolation (i.e. if you're trying to use it as a stand-alone definition of dukkha) because I suspect that to understand it you should also understand identity-view.