That first eyewitness account sounds rather implausible. Giant squid top out at 600 pounds. Southern right whale calves are already 15 feet long at birth, and probably weigh at least three or four tons.
So you think it’s a little fishy? 
Here are some size statistics for right whale calves (at birth), giant squid (the larger females) and colossal squid (possible estimate) from wikipedia.
Weight comparison:
Right whale calf - 907 kg
Giant squid (female) - 275 kg
Colossal squid (possibly) - 750 kg
Body length comparison:
Right whale calf - 4–6 m
Giant squid (female) - 13 m
Colossal squid (possibly) - 12–14 m
While the right whale calf is certainly a lot heavier than the giant squid, I don’t think that the calf’s weight difference compared with that of the colossal squid (if estimates are anywhere near accurate) is so great as to rule it out of hand. Both squid have considerable length advantage (or “reach”, perhaps, to use boxing parlance!). Then you’d have to take other factors into account like their comparative body strengths, the power of their water propulsion mechanisms, biological weaponry (in terms of tentacles, beaks, hooks, teeth), along with stamina and endurance.
Also potentially learned experience of such battles - a calf would perhaps not have been taught yet how to handle an encounter with a large squid by its mother (who we know teaches its young how to hunt). This article describes how whales have been observed catching squid by twisting themselves upside down just before grabbing their prey, creating a suction to vacuum squid into their mouths. I’d guess that this technique is a learned one from observation (of other whales, such as its mother) or perhaps experience (from hunting other, potentially smaller, squid).
Another learned experience might be to always attack a squid at its head/mantle-end, so as not to get a mouthful of teethy/hooky tentacles. Sperm whale’s echolation skills would give it an advantage in getting an element of surprise over the squid, who has only ocular vision. The whale would just have to make sure its angle-of-attack was towards the front end of the squid, relative to its direction of movement, and its surprise advantage would perhaps give it time to get into the best position to do so.
This article reports scientists’ belief that the eyes of the giant and colossal squid - the largest in the animal kingdom at 27cm (11in) across - have evolved precisely for early warning against enormous shapes, such as sperm whales. They found that the only benefit to having eyes, which are nutritionally “expensive”, of such large size was for spotting a “really large moving object”.
So I don’t think the first “eye-witness account” of a whale vs giant or colossal squid can be necessarily ruled out. The second account includes the problematical use of the word “strangled”, but that could just have been a literary description rather than a medical one, as I’d be skeptical as to to the feasibility of a squid tentacle being able to strangle a sperm whale in such a way as to deprive it of oxygen resulting in death.
If a colossal squid ever did get the better of a whale I wonder what the cause of death would be? Drowning, strangulation, suffocation (like a facehugger in Alien, but with an extra tentacle in the whale’s blowhole), exhaustion and/or trauma of getting nibbled to death by the squid’s pointy beak? I could imagine that if an angry colossal squid did manage to get itself firmly attached with all its tentacles to a whale, it wouldn’t be easy to shake off.
That article is about sperm whales eating squid. Right whales are baleen whales and don’t hunt or eat squid.
Can whales breathe through their mouths?
A whale’s trachea connects only to their blowhole(s) (some species have two) and can’t breathe through their mouths. A blowhole is basically a nostril and functions the same as your nose. Except whales really have trouble picking their “noses”.
It’s possible that even whale species that don’t hunt squid may have a learned awareness of the dangers of giant and colossal squid and have learned techniques to avoid possible threats, even if its as simple as an ability to recognise another animal as being potentially dangerous and to take evasive measures. A newborn calf might not have that.
I’m not saying the account is true, just that I don’t think that it’s impossible. I’d also conjecture that it’s not impossible that a mature colossal squid could be the aggressor in a battle between it and a newborn whale calf. From wikipedia:
No, there’s no connection between the windpipe and the throat but I wanted to get in the Alien facehugger imagery and found the idea of the squid suffocating the whale by sitting on the top of its head a little less compelling, as it would look a bit as though the whale was wearing the squid like a top hat or bishop’s mitre.
He could dive and crash his unwanted hat into a rock. :dubious: