Read the expression ?old delicious burdens.? A burden cannot be delicious.
The poet has used this combination of words to express that he has many
sweet memories of the people and places which he would like to remember
forever. The poet has used seemingly contradictory expressions to convey
the meaning that his heart is full of sweet memories of good and kind
people. Though he wants to be free from any type of attachment, he wants
to cherish these sweet memories in his heart forever.The expression contains opposite ideas that make it seem absurd or
unlikely, although it may be true. This is called ?Paradox

Dear Student 
Paradox, generally means  an absurd or contradictory statement or proposition which when investigated may prove to be well founded or true.
In this case the poet wants to cherish the sweet memories with people, however he also want to get rid of the same. Hence we can say that this is a paradox.

Regards

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