The Akkadians used cuneiforms much like Japanese use kanji (Chinese characters).

This means that the Akkadians could read a sign either with an approximation of how Sumerians had pronounced it or with the pronunciation of an Akkadian word that was a translation of the meaning of the original Sumerian word. Some signs did not correspond to the syllables that were pronounced, but they specified a class of things to which the word to which they were attached belonged.

Like in many other writing systems, the most ancient cuneiform signs were ideograms, which symbolized various things, like emojis now. Because at that time they had no phonetic meaning, we do not know which was the language of the writers, i.e. if it was Sumerian or some other language that may have been spoken in those places before Sumerian.

However, it is impossible to have a complete writing systems only with ideograms, where "complete" means that it can be used to write anything that you can communicate by speech.

So many centuries later, some of the signs that were used initially to designate a thing began to be used for any other thing that was pronounced in the same way, and eventually most signs were used to write syllables and the cuneiform writing system became a complete writing system. At the time when this transition from ideograms to phonograms happened, the language of the writers was Sumerian and the writing system became a mixture of syllabic signs and determinative signs.

As I mentioned above, after the Akkadians began to use the cuneiform signs they had their way to pronounce them. Because, like for Japanese texts, there are many alternatives for pronouncing the cuneiform signs, the correct deciphering of such texts is not easy.