Devotee: Did Kṛṣṇa have children by the gopīs?

Prabhupāda: No. Kṛṣṇa's love was not this love, sex love. That was different thing.

(Lecture on Bhagavad-Gita-------Los Angeles).

Devotee (3): Did Kṛṣṇa invent Rādhā for His own pleasure?

Prabhupāda: Yes. Not invent. Kṛṣṇa has nothing to invent. Everything is there. Invent means what was not in Him.

(Lecture on Srimad Bhagavatam--------London).

Devotee (1): I just didn't hear you correctly. Did you say that Śrī Kṛṣṇa Caitanya was playing Rādhā?

Prabhupāda: Yes, He is playing the part of Rādhārāṇī. He is worshiping Kṛṣṇa as Rādhārāṇī worshiped Kṛṣṇa. There is a verse composed by Lord Caitanya. He says,

āśliṣya vā pāda ratāṁ pinaṣṭu mām

(adarśanān) marma-hatāṁ karotu vā

yathā tathā vā vidadhātu lampaṭo

mat-prāṇa-nāthas tu sa eva nāparaḥ

(CC.3:20:47)

He's praying, "My Lord Kṛṣṇa, either You trample me down by Your feet, either You embrace me as lover, or You make me brokenhearted without Your presence. Whatever You like You can do. But still I am Your eternal servitor." So this attitude was Rādhārāṇī's. So Lord Caitanya is the feature of Kṛṣṇa understanding Rādhārāṇī. That Kṛṣṇa is great undoubtedly, but He thinks that Rādhārāṇī is greater than Him, because He cannot repay the loving transaction of Rādhā, of Kṛṣṇa. So he wanted to study what is there in Rādhārāṇī. "So I cannot study Rādhārāṇī in the feature of Kṛṣṇa. If I take the feature of Rādhārāṇī, then I can understand what are..." This is highest, I mean to say, transcendental sentiments. But Lord Caitanya is Rādhārāṇī's feature. Tad-dvayaṁ caikyam aptam. Caitanyākhyaṁ prakaṭam adhunā tad-dvayaṁ caityam āptam. Kṛṣṇa, when He wants to enjoy, He expands His pleasure potency, which is Rādhārāṇī. Now one Kṛṣṇa becomes two, Kṛṣṇa and His pleasure potency. And that pleasure potency, when unites with Kṛṣṇa, that is Caitanya. Kṛṣṇa becomes two, Rādhārāṇī and Kṛṣṇa. Kṛṣṇa cannot enjoy anything material because He is full in Himself. Therefore if He has to enjoy something, then that enjoyable personality must be expanded from Him only. So that is Rādhārāṇī. And when that enjoyable personality again takes into one, that is Caitanya. These things you'll understand as you develop Kṛṣṇa consciousness, in higher development stage. But it is, we can discuss. This is the fact. Yes?

(Lecture on Bhagavad-Gita----San Francisco).