The word bhagavān is explained thus by Parāśara Muni: one who is full in six opulences, who has full strength, full fame, wealth, knowledge, beauty and renunciation, is Bhagavān, or the Supreme Personality of Godhead. While Kṛṣṇa was present on this earth, He displayed all six opulences. Therefore great sages like Parāśara Muni have all accepted Kṛṣṇa as the Supreme Personality of Godhead.
(Bhagavad-Gita------10:1------purport).

The Supreme Lord is full in six opulences, and when a devotee approaches Him there is an exchange of these six opulences. The servant of the king enjoys on an almost equal level with the king. And so eternal happiness, imperishable happiness, and eternal life accompany devotional service. Therefore, realization of Brahman, or eternity, or imperishability, is included in devotional service. This is already possessed by a person who is engaged in devotional service.
(Bhagavad-Gita------14:27------purport).

Caitanya Mahāprabhu also gives evidence from Brahma-saṁhitā of the transcendental properties of Lord Kṛṣṇa's body:
īśvaraḥ paramaḥ kṛṣṇaḥ
sac-cid-ānanda-vigrahaḥ
anādir ādir govindaḥ
sarva-kāraṇa-kāraṇam
"Kṛṣṇa, who is known as Govinda, is the Supreme Godhead. He has an eternal, blissful spiritual body. He is the origin of all. He has no other origin, and He is the prime cause of all causes." (Bs. 5.1). In this way, Caitanya Mahāprabhu gives evidence that Kṛṣṇa is the original Personality of Godhead, full in all six opulences. It is Śrī Kṛṣṇa whose abode, known as Goloka Vṛndāvana, is the highest planetary system in the spiritual sky.
(Teachings of Lord Caitanya).

The prime difference between the Lord and the living entities is that the Lord is the creator and the living entities are the created. Here He is called the amogha-līlaḥ, which indicates that there is nothing lamentable in His creation. Those who create disturbance in His creation are themselves disturbed. He is transcendental to all material afflictions because He is full with all six opulences, namely wealth, power, fame, beauty, knowledge and renunciation, and thus He is the master of the senses. He creates these manifested universes in order to reclaim the living beings who are within them suffering threefold miseries, maintains them, and in due course annihilates them without being the least affected by such actions.
(Srimad Bhagavatam------1:3:36------purport).

The word Brahman means "the greatest," and when we speak of the greatest we immediately refer to the Supreme Personality of Godhead, the source of all emanations. Unless the greatest possesses six opulences in full, he cannot be called the greatest. The greatest, who is full in six opulences, is the Supreme Personality of Godhead. In other words, the Supreme Brahman is the Supreme Personality of Godhead as well.
(Teachings of Lord Caitanya).

The Lord is always full in six opulences, as mentioned herein: wealth, renunciation, fame, knowledge, strength and beauty. The word pūrtam means "in full." No one can claim that all wealth belongs to him, but Kṛṣṇa can claim it, since He has full wealth. Similarly, He is full in knowledge, renunciation, strength and beauty. He is full in everything, and no one can surpass Him. Another one of Kṛṣṇa's names is asamaurdhva, which means that no one is equal to or greater than Him.
(Srimad Bhagavatam------3:24:32------purport).

While Lord Caitanya was speaking to Sanātana Gosvāmī about the opulences of Kṛṣṇa, He was deep in ecstasy, and in that transcendental state He cited a verse from Śrīmad-Bhāgavatam (3.2.21) in which Uddhava, after the disappearance of Kṛṣṇa, told Vidura:
svayaṁ tv asāmyātiśayas tryadhīśaḥ
svārājya-lakṣmyāpta-samasta-kāmaḥ
baliṁ haradbhiś cira-lokapālaiḥ
kirīṭa-koṭyeḍita-pādapīṭhaḥ
"Kṛṣṇa is the master of all demigods, including Lord Brahmā, Lord Śiva and the expansion of Viṣṇu within this universe. Therefore no one is equal to or greater than Him, and He is full in six opulences. All the demigods engaged in the administration of each universe (brahmāṇḍa) offer their respectful obeisances unto Him. Indeed, the helmets on their heads are beautiful because they are decorated with the imprints of the lotus feet of the Supreme Lord."
(Teachings of Lord Caitanya).

In defining the Supreme Personality of Godhead, we say that He is full in all six opulences—wealth, fame, strength, influence, beauty and renunciation. He is called renounced because He is not attached to anything in this material world; He is specifically attached to the spiritual world and the living entities there.
(Srimad Bhagavatam------5:19:6------purport).

The Supreme Personality of Godhead, Lord Kṛṣṇa, is always full with six opulences—namely complete wealth, complete strength, complete fame, complete knowledge, complete beauty and complete renunciation. The Lord appears in different complete, eternal forms of incarnation.
(Krsna Book).

Brahman indicates that the greatest is full with six opulences; the Supreme Personality of Godhead is the reservoir of all wealth, all fame, all strength, all beauty, all knowledge and all renunciation. When Lord Kṛṣṇa was present personally on earth, He exhibited these six opulences in full. No one was richer than Lord Kṛṣṇa, no one was more learned than Him, no one more beautiful, no one stronger, no one more famous and no one more renounced. Therefore the Supreme Personality of Kṛṣṇa is the Supreme Brahman.
(Teachings of Lord Caitanya).

There are innumerable Vaikuṇṭha planets, innumerable incarnations, expansions of the Supreme Lord, and innumerable universes also, and of all these existences the Supreme Lord Kṛṣṇa is the only source. His transcendental body is composed of eternity, bliss and knowledge, and He is known as the son of Mahārāja Nanda and the inhabitant of Goloka Vṛndāvana. He is full with six opulences—all wealth, strength, fame, beauty, knowledge and renunciation.
(Teachings of Lord Caitanya).

When the Yamunā was threatened like this, she became greatly afraid of the power of Balarāma and immediately came in person, falling at His lotus feet and praying thus: "My dear Balarāma, You are the most powerful personality, and You are pleasing to everyone. Unfortunately, I forgot Your glorious, exalted position, but now I have come to my senses, and I remember that You hold all the planetary systems on Your head merely by Your partial expansion Śeṣa. You are the sustainer of the whole universe. My dear Supreme Personality of Godhead, You are full with six opulences. Because I forgot Your omnipotence, I have mistakenly disobeyed Your order, and thus I have become a great offender. But, my dear Lord, please know that I am a soul surrendered unto You, who are very affectionate to Your devotees. Therefore please excuse my impudence and mistakes, and, by Your causeless mercy, may You now release me."
(Krsna Book).