I assume that each member of the Godhead loves each other member of the Godhead. God is, after all, love (1 John 4:8 and 16).
The Gospels are quite explicit regarding the love which God the Father has for God the Son. Jesus himself makes this very clear (John 3:35; and 5:20). Moreover, the voice coming out of heaven at Jesus' baptism addresses the Son as "My beloved Son" (Luke 3:22; Matthew 3:17; and Mark 1:11). (True enough, the voice from heaven is not linked specifically to the Father, but the word Beloved is clearly linked to the Son, not the Father or the Spirit.)
One could say quite accurately that Jesus proved his love for the Father in everything he did and said while he was on earth. On more than one occasion, Jesus made this devotion to his Father's will quite explicit:
"My food is to do the will of Him who sent Me and to accomplish His work" (John 4:34).
". . . he that sent me is with me: the Father hath not left me alone; for I do always those things that please him" (John 8:29 KJV).
Logically, then, one could also say that Jesus proved he loved the Father by doing His will and by obeying Him. In the same way the apostle James emphasized the role which works play in the faith/works duo, perhaps by analogy Jesus in his way of life emphasized the role which loving obedience played in the love/works duo.
In this regard, the apostle John, the "apostle of love" and "the disciple whom Jesus loved," said,
We know love by this, that He laid down His life for us; and we ought to lay down our lives for the brethren. Little children, let us not love with word or with tongue, but in deed and truth" (1 John 3:17-18).
In other words, saying "I love you" to someone is much easier than demonstrating your love for the same person by performing a loving action such as feeding or clothing him, visiting him when he is on his sickbed, comforting him when he has recently lost a loved one through death, or forgiving him when he has sinned against you.
I have no doubt that Jesus loves his Father, but I am curious as to why that love is not stated as explicitly in the Gospels as is the love of the Father for his Son. I suppose a good answer to my question would draw from both Testaments and would be framed in terms which are consistent with the Father-Son relationship which is foreshadowed in the Tanakh (e.g., in Psalm 2) but revealed more fully in the New Covenant.