Sure, the blue whale (Balaenoptera musculus), a marine mammal belonging to the baleen whales (Mysticeti), is big. We mean really big! And it is bigger than any other extant animal, and it’s more massive than the most massive animal to have ever existed. But the sperm whale is not the largest living thing on Earth.
According to Wikipedia, the largest living thing on Earth is not a whale or a giant octopus, but a stand of Aspen trees in Utah. PRI.org notes,
Called “Pando,” which is Latin for “I spread,” the group of quaking aspens is considered one of the largest — by area — and most massive living organisms on earth. The quaking aspen, found from coast to coast across North America, grows in groups called stands. Within these stands, a single tree will spread by sprouting new stems from its roots, often several feet from the original trunk.
“Those trees remain connected for a good long while,” explains Jennifer DeWoody, a geneticist with the US Forest Service. “This long process is over many years — suckers [or stems] coming up over a larger and larger area.” Their stems can share the products of photosynthesis, food, and possibly disease as well.
Because individual aspen stems generally live about 100-150 years, DeWoody says the origin mother stem is likely dead: “The only way the whole clone survives is to send up new suckers,” she says. While other trees can also clone in this way, “[aspens] do it the most broadly across so many different environments.”