TRSM[k_,b_]:=b Sum[2(i-1)+1,{i,1,k}]

TRSM[k,b]

SYRK[k_,b_]:=k b (b+1)

SYRK[k,b]

CHOL2[m_]:=
Sum[
TRSM[i,1]+SYRK[i,1]+1,
{i,0,m-1}]

CHOL2[m]//Expand

CHOL[m_,b_]:=
Sum[
TRSM[i,b]+SYRK[i,b]+CHOL2[b],
{i,0,m-b,b}]

CHOL[m,b]/.Floor[x_]->x//Expand

Sum[TRSM[i,b],{i,0,m-b,b}]/.Floor[x_]->x//Expand
Sum[SYRK[i,b],{i,0,m-b,b}]/.Floor[x_]->x//Expand
Sum[CHOL2[b],{i,0,m-b,b}]/.Floor[x_]->x//Expand