In this poem, the tattoo works as a two-layer symbol: first of all, as an actual tattoo it is a mark used by the nazis to number the jews they sent to concentration camps. This is the historical period reflected in the poem.
The second layer is the tattoo as a permanent mark for the person who bears it. They are usually made voluntarily and in order to remember some impotant achievement or experience, to express an emotion.
In this case, the numbers "3-7-8-2-5" tattooed in his father's arm was imposed during the Holocaust, and as a survivor it still marks his life and his experiences. Having survived the horrors of the Holocaust, he tries to protect and embrace his child the best he can, to the point of "bone-crushing", but he does not speak aboutit, neither does his child dare to ask about the tattoo or his experiences.
The Holocaust has marked the father's life to the point that both father and son "don't breath the same air", and his inner scars, like the permanent reminder of the tattoo "still bleed". That is why the speaker of the poem wishes he could absorve his father's pain and "scrub the numbers from his flesh", the symbol of the permanent anguish of the Holocaust survivor.