Balarama is not usually referred to as Vāsudeva, but there is one use of Vāsudeva in the Bhagavad Gita which many commentators interpret as referring to Balarama. Namely verse 10.37:
vṛṣṇīnāṁ vāsudevo ’smi pāṇḍavānāṁ dhanañ-jayaḥ |
munīnām apy ahaṁ vyāsaḥ kavīnām uśanā kaviḥ ||
Of the descendants of Vṛṣṇi I am Vāsudeva, and of the Pāṇḍavas I am Arjuna. Of the sages I am Vyāsa, and among great thinkers I am Uśanā.
Now to say that Vāsudeva refers to Krishna, as usual, would be to concede that Krishna is an incarnation of Vishnu, which some sects are unwilling to do as they view Krishna as supreme. So they instead interpret Vāsudeva as Balarama. Here is what Sridhara Swami says in his commentary on the Bhagavad Gita:
Of the Vrishnis or His apparent lineage, Lord Krishna’s vibhuti or divine, transcendental opulence is Vasudeva which means the son of Vasudeva. It would not be acceptable for Lord Krishna to be naming Himself because He is describing His vibhuti and so the only other son of Vasudeva is Balarama who is Lord Krishna’s first and foremost expansion and who expands as all the other incarnations with the exception of Narayana the ruler of all the spiritual planets in the spiritual realm of Vaikuntha who is Lord Krishna’s direct expansion.
Here is what Keshava Kashmiri says:
Among the descendants of the Vrishni lineage Lord Krishna’s vibhuti or divine, transcendental opulence is the son of Vasudeva. As Lord Krishna is describing His vibhuti it is not logical that He would be would be referring to Himself. The only other son of Vasudeva is Balarama who is the first expansion of Lord Krishna and the direct source of all other avataras or incarnations including Rama and Vishnu. So Lord Krishna’s vibhuti as the son of Vasudeva is the all powerful Balarama.
And here is what Srila Prabhupada says:
Krishna is the original Supreme Personality of Godhead, and Baladeva is Krishna’s immediate expansion. Both Lord Krishna and Baladeva appeared as sons of Vasudeva, so both of Them may be called Vasudeva. From another point of view, because Krishna never leaves Vrindavana, all the forms of Krishna that appear elsewhere are His expansions. Vasudeva is Krishna’s immediate expansion, so Vasudeva is not different from Krishna. It is to be understood that the Vasudeva referred to in this verse of Bhagavad-gita is Baladeva, or Balarama, because He is the original source of all incarnations and thus He is the sole source of Vasudeva.