CC Madhya 4.77
tāṅra hasta-sparśe punaḥ temani ha-ila
Although Śrī Gopāla ate everything offered, still, by the touch of His transcendental hand, everything remained as before.
The atheists cannot understand how the Supreme Personality of Godhead, appearing in the form of the Deity, can eat all the food offered by His devotees. In the Bhagavad-gītā (9.26) Kṛṣṇa says:
tad ahaṁ bhakty-upahṛtam aśnāmi prayatātmanaḥ
“If one offers Me with love and devotion a leaf, a flower, a fruit or water, I will accept it.” The Lord is pūrṇa, complete, and therefore He eats everything offered by His devotees. However, by the touch of His transcendental hand, all the food remains exactly as before. It is the quality that is changed. Before the food was offered, it was something else, but after it is offered the food acquires a transcendental quality. Because the Lord is pūrṇa, He remains the same even after eating. Pūrṇasya pūrṇam ādāya pūrṇam evāvaśiṣyate. The food offered to Kṛṣṇa is qualitatively as good as Kṛṣṇa; just as Kṛṣṇa is avyaya, indestructible, the food eaten by Kṛṣṇa, being identical with Him, remains as before.
Apart from this, Kṛṣṇa can eat the food with any one of His transcendental senses. He can eat by seeing the food or by touching it. Nor should one think that it is necessary for Kṛṣṇa to eat. He does not become hungry like an ordinary human being; nonetheless, He presents Himself as being hungry, and as such, He can eat everything and anything, regardless of quantity. The philosophy underlying Kṛṣṇa’s eating is understandable by our transcendental senses. When our senses are purified by constantly being engaged in the devotional service of the Lord, we can understand Kṛṣṇa’s activities, names, forms, qualities, pastimes and entourage.
sevonmukhe hi jihvādau svayam eva sphuraty adaḥ
“No one can understand Kṛṣṇa by the blunt material senses. But He reveals Himself to the devotees, being pleased with them for their transcendental loving service unto Him.” (Bhakti-rasāmṛta-sindhu 1.2.234) The devotees understand Kṛṣṇa through revelation. It is not possible for a mundane scholar to understand Kṛṣṇa and His pastimes through research work on the nondevotional platform.