SB 10.8.13

āsan varṇās trayo hy asya
 gṛhṇato ’nuyugaṁ tanūḥ
śuklo raktas tathā pīta
 idānīṁ kṛṣṇatāṁ gataḥ
Synonyms: 
āsan — were assumed; varṇāḥ trayaḥ — three colors; hi — indeed; asya — of your son Kṛṣṇa; gṛhṇataḥ — accepting; anuyugam tanūḥ — transcendental bodies according to the different yugas; śuklaḥ — sometimes white; raktaḥ — sometimes red; tathā — as well as; pītaḥ — sometimes yellow; idānīm kṛṣṇatām gataḥ — at the present moment He has assumed a blackish color.
Translation: 
Your son Kṛṣṇa appears as an incarnation in every millennium. In the past, He assumed three different colors — white, red and yellow — and now He has appeared in a blackish color. [In another Dvāpara-yuga, He appeared (as Lord Rāmacandra) in the color of śuka, a parrot. All such incarnations have now assembled in Kṛṣṇa.]
Purport: 

Partially explaining the position of Lord Kṛṣṇa and partially covering the facts, Garga Muni indicated, “Your son is a great personality, and He can change the color of His body in different ages.” The word gṛhṇataḥ indicates that Kṛṣṇa is free to make His choice. In other words, He is the Supreme Personality of Godhead and may therefore do whatever He desires. In Vedic literature the different colors assumed by the Personality of Godhead in different millenniums are stated, and therefore when Garga Muni said, “Your son has assumed these colors,” he indirectly said, “He is the Supreme Personality of Godhead.” Because of Kaṁsa’s atrocities, Garga Muni tried to avoid disclosing this fact, but he indirectly informed Nanda Mahārāja that Kṛṣṇa, his son, was the Supreme Personality of Godhead.

It may be noted that Śrīla Jīva Gosvāmī, in his book Krama-sandarbha, has enunciated the purport of this verse. In every millennium, Kṛṣṇa appears in a different form, either as white, red or yellow, but this time He personally appeared in His original, blackish form and, as predicted by Garga Muni, exhibited the power of Nārāyaṇa. Because in this form the Supreme Personality of Godhead exhibits Himself fully, His name is Śrī Kṛṣṇa, the all-attractive.

Factually, Kṛṣṇa is the source of all avatāras, and therefore all the different features of the different avatāras are present in Kṛṣṇa. When Kṛṣṇa incarnates, all the features of other incarnations are already present within Him. Other incarnations are partial representations of Kṛṣṇa, who is the full-fledged incarnation of the Supreme Being. It is to be understood that the Supreme Being, whether appearing as śukla, rakta or pīta (white, red or yellow), is the same person. When He appears in different incarnations, He appears in different colors, just like the sunshine, which contains seven colors. Sometimes the colors of sunshine are represented separately; otherwise the sunshine is observed mainly as bright light. The different avatāras, such as the manvantara-avatāras, līlā-avatāras and daśa-avatāras, are all included in the kṛṣṇa-avatāra. When Kṛṣṇa appears, all the avatāras appear with Him. As described in Śrīmad-Bhāgavatam (1.3.26):

avatārā hy asaṅkhyeyā
 hareḥ sattva-nidher dvijāḥ
yathāvidāsinaḥ kulyāḥ
 sarasaḥ syuḥ sahasraśaḥ

The avatāras incessantly appear, like incessantly flowing water. No one can count how many waves there are in flowing water, and similarly there is no limitation of the avatāras. And Kṛṣṇa is the full representation of all avatāras because He is the source of all avatāras. Kṛṣṇa is aṁśī, whereas others are aṁśa, part of Kṛṣṇa. All living entities, including us, are aṁśas (mamaivāṁśo jīva-loke jīva-bhūtaḥ sanātanaḥ). These aṁśas are of different magnitude. Human beings (who are minute aṁśas) and the demigods, viṣṇu-tattva and all other living beings are all part of the Supreme. Nityo nityānāṁ cetanaś cetanānām (Kaṭha Upaniṣad 2.2.13). Kṛṣṇa is the full representation of all living entities, and when Kṛṣṇa is present, all avatāras are included in Him.

The Eleventh Canto of Śrīmad-Bhāgavatam describes the incarnations for each yuga in chronological order. The Bhāgavatam says, kṛte śuklaś catur-bāhuḥ, tretāyāṁ rakta-varṇo’sau, dvāpare bhagavān śyāmaḥ and kṛṣṇa-varṇaṁ tviṣākṛṣṇam. We actually see that in Kali-yuga, Bhagavān has appeared in pīta-varṇa, or a yellow color, as Gaurasundara, although the Bhāgavatam speaks of kṛṣṇa-varṇam. To adjust all these statements, one should understand that although in some yugas some of the colors are prominent, in every yuga, whenever Kṛṣṇa appears, all the colors are present. Kṛṣṇa-varṇaṁ tviṣākṛṣṇam: although Caitanya Mahāprabhu appears without kṛṣṇa, or a blackish color, He is understood to be Kṛṣṇa Himself. Idānīṁ kṛṣṇatāṁ gataḥ. The same original Kṛṣṇa who appears in different varṇas has now appeared. The word āsan indicates that He is always present. Whenever the Supreme Personality of Godhead appears in His full feature, He is understood to be kṛṣṇa-varṇam, although He appears in different colors. Prahlāda Mahārāja states that Caitanya Mahāprabhu is channa; that is, although He is Kṛṣṇa, He is covered by a yellow color. Thus the Gauḍīya Vaiṣṇavas accept the conclusion that although Caitanya Mahāprabhu appeared in pīta color, He is Kṛṣṇa.

kṛṣṇa-varṇaṁ tviṣākṛṣṇaṁ
 sāṅgopāṅgāstra-pārṣadam
yajñaiḥ saṅkīrtana-prāyair
 yajanti hi sumedhasaḥ

(Bhāg. 11.5.32)